The Hydrogen Mixing Portal, Its Origins, and Its Cosmological Effects
TThe Hydrogen Mixing Portal, Its Origins, and Its Cosmological Effects
Lucas Johns
1, 2, ∗ and Seth Koren
3, 4, † Departments of Astronomy and Physics, University of California, Berkeley, CA 94720, U.S.A. Department of Physics, University of California, San Diego, CA 92093, U.S.A. Enrico Fermi Institute, University of Chicago, Chicago, IL 60637, U.S.A. Department of Physics, University of California, Santa Barbara, CA 93106, U.S.A.
Hydrogen oscillation into a dark-sector state H (cid:48) has recently been proposed as a novel mechanismthrough which hydrogen can be cooled during the dark ages—without direct couplings betweenthe Standard Model and dark matter. In this work we demonstrate that the requisite mixing canappear naturally from a microphysical theory, and argue that the startling deviations from standardcosmology are nonetheless consistent with observations. A symmetric mirror model enforces thenecessary degeneracy between H and H (cid:48) , and an additional ‘twisted’ B + L (cid:48) symmetry dictatesthat H – H (cid:48) mixing is the leading connection between the sectors. We write down a UV completionwhere ∼ TeV-scale leptoquarks generate the partonic dimension-12 mixing operator, thus linking tothe energy frontier. With half of all H atoms oscillating into H (cid:48) , the composition of the universe isscandalously different during part of its history. We qualitatively discuss structure formation: boththe modifications to it in the Standard Model sector and the possibility of it in the mirror sector,which has recently been proposed as a resolution to the puzzle of early supermassive black holes.While the egregious loss of SM baryons mostly self-erases during reionization, to our knowledge thisis the first model that suggests there should be ‘missing baryons’ in the late universe, and highlymotivates a continued, robust observational program of high-precision searches for cosmic baryons. I. INTRODUCTION
The dark ages of the universe—the hundreds of mil-lions of years after recombination but before cosmicdawn, during which halos, galaxies, and finally the firststars take shape—remain one of the most observationallymysterious epochs of our universe’s chronology. The eraof 21 cm cosmology is upon us, however, and observa-tories both current and coming promise unprecedentedaccess to this long expanse of cosmic history.Along with those promises comes the possibility fornew fundamental physics discoveries. Scenarios predict-ing 21 cm signatures are diverse, encompassing dark mat-ter (DM) decay, annihilation, and warmth [1–17]; cosmicstrings [18–21]; primordial black holes [22–25]; and darkenergy [26–31]. No doubt even more applications will berecognized as the field continues to advance.New fundamental physics may have already been dis-covered by the Experiment to Detect the Global Epochof Reionization Signature (EDGES), which reported anabsorption feature at redshift z ∼
17 with at least twicethe depth of the standard ΛCDM prediction [32], a 3 . σ deviation [33, 34]. The publication of this result was fol-lowed by the quick realization that interactions of DMwith electrons and/or protons could be responsible forcooling the hydrogen gas beyond the extent expectedfrom adiabatic expansion alone [34–37]. However, sucha possibility faces severe constraints from a variety ofsources. Interactions of DM with charged particles isconstrained both by early-time measurements of the cos-mic microwave background and by late-time direct and ∗ NASA Einstein Fellow ([email protected]) † EFI Oehme Fellow ([email protected]) indirect detection experiments. Within the well-exploredscenarios, the only way for such interactions to be respon-sible for the EDGES signal is for the interacting DM tobe only a small subcomponent of the full DM density.Additional strict requirements on the mass and interac-tion strength, as well as some further contortions, arerequired to ensure that these scenarios are self-consistent(see e.g. [33, 37–41] for discussions).A more conservative move is to attribute the surpris-ing absorption amplitude to unknown astrophysics, buthere, too, contortions are evidently required. These pro-posals posit the existence of high- z sources that drive theradio background above the level from cosmic microwavebackground (CMB) photons. While such interpretationsof the EDGES data draw support from results reportedby ARCADE-2 and the Long Wavelength Array, the chal-lenge is again self-consistency. Early star-forming galax-ies can enhance the radio background, but to match theEDGES data they must be ∼ z counter-parts, assuming that relations between radio emissivityand star-formation rate (SFR) in present-day galaxies ex-trapolate to higher redshifts [42]. Furthermore, electronsaccelerated by the supernovae of Population III stars—which could conceivably give rise to this emission via syn-chrotron radiation—are accompanied by cosmic rays thatheat the intergalactic medium (IGM) and tend to offsetthe effect of making the backlight brighter [43]. Anotherpossible source of synchrotron-radiating electrons, radio-loud black hole accretion, must occur in highly obscuredenvironments to avoid excessive heating of the IGM. Eventhen these sources are beset by inverse Compton scat-tering of electrons on CMB photons, though whetherthey must be orders of magnitude radio-louder than theircounterparts today is a matter of ongoing debate [44–46]. a r X i v : . [ h e p - ph ] D ec At this time, the question of the viability of a strong radioexcess can only be said to be unsettled.The most conservative view of all is that the EDGESanomaly is an artifact of the data analysis. There hasbeen spirited discussion regarding this possibility [47–53]. It appears that a decisive verdict will have to await(dis)confirmation from future experiments. Thankfully,the 21 cm revolution is just beginning, with numerousambitious projects underway or under development. Fu-ture measurements of the sky-averaged signal by DARE[54], LEDA [55], PRI Z M [56], SARAS [57], and REACH[58] will be able to confirm the presence of the anomalousabsorption feature, while other upcoming experimentssuch as HERA [59], OVRO-LWA [60], and SKA1-LOW[61] will measure the power spectrum of 21 cm fluctua-tions. Measurements of the line intensity of other atoms,such as helium [62–65], molecular hydrogen [66] and deu-terium [67, 68] provide complementary views of cosmicdawn, as outlined in recent community reports [69–71].We refer to the recent work Ref. [72] for a review of ob-servational methods and challenges with a focus on thekey ingredient of data analysis.In the meantime the anomaly persists, and it is worthconsidering how else it might be produced. While be-yond the Standard Model (BSM) scenarios have beenproposed that generate a radio excess [40, 73–77], in thiswork we embrace the baryon cooling interpretation. Wehave recently proposed hydrogen oscillations into a darkstate as a novel mechanism through which baryon coolingmay take place [78]. This allows such cooling without re-quiring any direct interactions between SM particles andDM. It is only neutral atomic hydrogen which picks upan effective interaction with DM, and this interaction isonly active over cosmological timescales and only in therelatively quiescent intergalactic medium—automaticallyrestricting the effects to the dark ages between recombi-nation and reionization. In [78] we established that thismechanism can indeed cool hydrogen to the level sug-gested by EDGES, but did not discuss the microphysicalorigins of such mixing nor its effects past the EDGES sig-nal. We herein take up both these topics: grounding themechanism in sensible particle physics and preliminarilyexploring the effects of dark age mixing on the formationof structures and stars.This mechanism can in fact be naturally accommo-dated within the well-motivated framework of a mirrormodel, where the necessary features can be symmetry-protected. In a mirror model there is a Z symmetryrelating the SM gauge groups and field content to an-other dark, ‘mirror’ sector. Such models have a long andstoried history, having been first suggested in passing byLee and Yang in 1956 [79]. We refer the reader to thehistorical review by Okun [80] for further references, butmention that mirror matter was first connected to darkmatter by Blinnikov and Khlopov in 1982 [81], was sug-gested to appear naturally from the heterotic string bythe Princeton string quartet in 1984 [82], and was firstwritten down in full with unbroken symmetry by Foot, Lew, and Volkas in 1991 [83]. In recent years closely-related structures have seen intense study after beingconnected to the hierarchy problem by Chacko, Goh, andHarnik in 2005 [84].In a mirror model with unbroken Z symmetry, there isa mirror hydrogen state which is exactly degenerate withSM hydrogen. As a result, if these states have just a smallamount of mass mixing, the SM hydrogen which formsduring recombination will gradually oscillate into mir-ror hydrogen, bearing out the phenomenology discussedin [78]. Mirror hydrogen’s interactions with dark mat-ter are then effectively inherited by SM hydrogen overcosmologically-long timescales. In particular, over thedark ages hydrogen can lose energy to the dark sector.Below we will assume for simplicity that the mirror sectoris unpopulated before hydrogen begins oscillating into it,though we note that our qualitative results are robustto the inclusion of a subdominant mirror sector compo-nent. With unbroken Z symmetry in the Lagrangian,this asymmetry is most easily set up by appealing to cos-mic variance: it traces back to quantum fluctuations inthe early universe in our Hubble patch, while the theoryitself remains symmetric.In the scenario we consider, communication betweenthe SM and dark sectors passes predominantly throughthe hydrogen portal. Being neutral in the SM, a hy-drogen atom violates no gauge symmetries when it oscil-lates into mirror hydrogen. But the same is true of theneutron. We thus need to justify why the hydrogen por-tal might predominate—or, indeed, even be relevant—despite its suppressions from both proton–electron wave-function overlap and the high mass dimension of thehydrogen–mirror hydrogen mixing operator. We arguebelow that such a theory is indeed sensible if a ‘twisted’ B + L (cid:48) symmetry is imposed. We exhibit a plausible UVcompletion by introducing the appropriate leptoquarkssuch that hydrogen oscillations are permitted but neu-tron oscillations and proton decay are not. As it turnsout, the very small mixing parameter that arises from lep-toquarks with masses around the TeV-scale energy fron-tier puts us right in the neighborhood of cosmologicaltimescales.The question, then, is whether in-medium hydrogenoscillations are consistent with what we know about thecosmic timeline. In [78] we showed that there is in-deed ample parameter space where in-medium mixingis efficient enough to account for the cooling suggestedby EDGES. However, making a significant fraction ofbaryons temporarily disappear from the universe is a newidea, as far as we know, and a radical one on the face ofit. The baryon density in the early universe is preciselyknown from cosmological measurements. In the localuniverse, tallying the various populations of baryons is We use this term to refer specifically to the hydrogen mixing portal, which is distinct from the hydrogen decay portal recentlyintroduced in Ref. [85]. challenging and uncertain. Still, in light of recent mea-surements of the warm–hot intergalactic medium, wherea significant fraction of baryons now reside, reducing thelocal baryon density by a full factor of 2 is a no-go. Ifhalf of all baryons are to disappear during the dark ages,they must find their way back by the current era.As it happens, reionization naturally shepherds mostof the baryons back to our sector of the universe. Ifthe mixing portal is in equilibrium during the epoch ofreionization, it holds the abundances of SM and mirrorhydrogen equal, so that the reionization of SM hydrogenleads to an effective depletion of the abundance of mirrorhydrogen. As a result, the drastically different composi-tion of the universe during the dark ages naturally hidesitself. There will be some extant baryons trapped as relicmirror hydrogen in the late universe, but we do not ex-pect them to conflict with the tallies mentioned above.On the contrary, they may even be connected to the partof the longstanding missing baryons problem that stillremains.The temporary conversion of hydrogen into mirror hy-drogen is likely to have other observable effects besideslowering the gas temperature at cosmic dawn. We takeup this topic in a preliminary and qualitative way, sur-veying the relevance of H cooling, mirror stars, direct-collapse black holes, streaming velocities, and probes ofreionization. These issues are complex, intertwined, anddeserving of further investigation.We begin Sec. II with an overview of the pertinentparts of 21 cm cosmology, then analyze the physics ofthe hydrogen portal in the dark ages, providing addi-tional detail omitted from [78]. In Sec. III we addresshow the desired mixing phenomenology might arise froman underlying particle physics model. We then turn inSec. IV to a discussion of other astrophysical and cosmo-logical implications, before concluding in Sec. V. II. COSMOLOGICAL EVOLUTION
Between the epochs of recombination and reionization,most of the baryons in the universe are in the form ofneutral atomic hydrogen. The spin temperature T S isdefined in relation to the density ratio of the F = 1 and F = 0 ground-state hyperfine levels: n n = 3 exp (cid:18) − T hf T S (cid:19) , (1)where T hf ∼ = 68 mK is the hyperfine splitting expressedas a temperature and the factor of 3 is the degeneracy ra-tio of the two levels. Because T S is set by a competitionamong different interactions, it does not always track thebrightness temperature T R of the radiation illuminatingthe gas. This makes hydrogen visible against its back-ground at some redshifts [86].Experiments like EDGES are sensitive to the red-shifted (and frequency-dependent) differential brightness temperature T = T obs − T R z = T S − T R z (cid:0) − e − τ (cid:1) . (2)Here T obs = T S (1 − e − τ ) + T R e − τ is the observed bright-ness temperature and τ is the optical depth of the hy-drogen gas. In words, T measures the change in bright-ness temperature of the microwave background due toabsorption and re-emission by hydrogen gas en route toEarth. While an absorption feature in T was antici-pated by EDGES, the depth of the feature was not. Weare proposing that mixing between SM hydrogen H andmirror hydrogen H (cid:48) can explain the anomaly. In this sec-tion we first describe qualitatively how mixing alters thecosmic timeline, then move on to a quantitative analysisof the dynamics of mixing and cooling. A. Cosmic Timeline and Evolution of theHydrogen Spin Temperature
The spin temperature tracks the equilibrium set bythe competition of induced hyperfine transitions, atomiccollisions, and resonant scattering of Ly α photons [87]: T − S = T − R + x c T − g + x α T − α x c + x α . (3) x c and x α are coefficients that quantify the relative im-portance of collisions and spin flip via Ly α transitions.They respectively couple T S to the kinetic temperature T g of the gas and to the color temperature T α of the Ly α radiation field.In the standard cosmology (see Fig. 1), the sky-averaged spin temperature, which we’ll continue to de-note simply with T S , passes through several qualita-tively distinct stages as the universe expands. In theaftermath of recombination, CMB photons constitutethe 21 cm radiation field and keep the hydrogen gas at T g = T R = T CMB through the combination of Comp-ton scattering of CMB photons on residual free electronsand collisions of those electrons with hydrogen atoms. T S therefore follows T R until the gas drops out of thermalequilibrium with the CMB at z ∼ − T g —and with it T S —todrop below T R . At z ∼ −
40, however, collisional cou-pling becomes inefficient, and subsequent evolution of T S is driven by interactions with the radiation field.The standard expectation is that at cosmic dawn hy-drogen is visible in absorption, it being colder than theCMB backlight ( T g ∼ = 7 K vs. T CMB ∼ = 49 K at z = 17,for example). The amplitude of the trough is maximizedwhen T S is closely coupled to T g by the Wouthuysen–Field effect, which is to say by the resonant scattering ofLy α photons [87, 88]. In that extreme case, the depth at z = 17 is anticipated to be T ∼ = −
210 mK. EDGES, incontrast, observed a trough spanning 20 (cid:38) z (cid:38)
15 andreaching a maximum amplitude of T = − +200 − mK(99% C.L.) at z ∼ = 17. This finding has been var-iously interpreted as revealing super-adiabatic coolingof the gas, non-CMB background sources, or system-atic/experimental error. Our proposal falls in the firstgroup.In the presence of H – H (cid:48) mixing, oscillations begin oncethe ionization fraction drops at recombination. Quan-tum superpositions of H and H (cid:48) are continuously de-cohered by collisional processes. The equilibrium towhich this tends is an equipartition of number density n H = n H (cid:48) . If mixing equilibrates during the dark ages,the SM hydrogen density is thus cut in half.Sometime after recombination, H – H (cid:48) mixing comesinto equilibrium and equalizes the mirror and SM hydro-gen densities. After the SM gas thermally decouples fromthe CMB, the mirror gas loses thermal energy throughits interactions with DM. This cooling is carried over tothe SM sector by the rapid interconversion of H and H (cid:48) ,causing T g to dip below the green curve shown in Fig. 1.By cosmic dawn, the SM gas has been cooled to the ex-tent required to explain the EDGES anomaly. Finally,the universe reionizes. Provided that mixing continues tobe in equilibrium during this last epoch, n H (cid:48) will trackthe falling density of neutral SM atoms and the baryonswill be returned to our sector.We emphasize, in distinction with other DM-assistedcooling models, that at the end of the dark ages the SMhydrogen gas is both colder and more dilute in the H – H (cid:48) mixing scenario than it is in the standard (non-BSM) one.Since the optical depth τ is small, T is approximatelyproportional to τ = 3 A n H ν T S H ( z ) , (4)where A = 2 . × − s − is the spontaneous emis-sion coefficient for the 21 cm hyperfine transition, ν =1 .
42 GHz is its rest-frame frequency, and H ( z ) is theHubble rate. (From here on we will be dropping theexplicit argument of this last quantity, but it will beclear from the context whether the Hubble rate or thehydrogen symbol is being referred to.) Plugging this intoEq. (2) and assuming that T S = T g , consistency with theEDGES best-fit amplitude implies that SM–DM interac-tions cool the gas down to a temperature [33] T SM − DM g ( z = 17) ∼ = 3 . . (5)Mixing equilibration, on the other hand, requires the gasto cool by an additional factor of ∼ T H − H (cid:48) g ( z = 17) ∼ = 1 . . (6) Prior to and during recombination, the operator giving rise tomixing permits passage through the portal via e + p −→ e (cid:48) + p (cid:48) ,but only at an extremely low level. Given the mixing parameterswe focus on, conversion of H to H (cid:48) during recombination is alsonegligible. See Sec. IV B for more discussion. This number constrains the properties of DM, as we dis-cuss below, but it makes no direct demands on H – H (cid:48) oscillations. All that is required of the latter is that theyachieve mixing equilibrium at the appropriate times. B. Dynamics of the Hydrogen Portal
The nonequilibrium dynamics of H – H (cid:48) mixing is de-scribed by the quantum kinetic equation i dρdt = [ H , ρ ] + i C . (7) ρ is a 2 × H and H (cid:48) and whose off-diagonal entries encode the quan-tum coherence between the two states. (We assume thatthe singlet and triplet hyperfine states do not substan-tially differ in their mixing with their respective mirrorcounterparts, though we will mention in Sec. III the pos-sibility that they vary.) H is the Hamiltonian and C isthe collision term.The Hamiltonian has the form H = (cid:18) E H + ∆ V δδ E H (cid:48) − ∆ V (cid:19) , (8)where E H ( H (cid:48) ) is the energy of (mirror) hydrogen in vac-uum; ∆ V = ( V H − V H (cid:48) ) / V H ( H (cid:48) ) from H ( H (cid:48) ) forward scatter-ing; and δ is the mixing parameter. Following the con-vention in the neutrino literature, we parameterize themixing in terms of an in-medium oscillation frequency ω m = (cid:113) (∆ E + ∆ V ) + δ , (9)where ∆ E = (cid:0) E H − E H (cid:48) (cid:1) /
2, and an in-medium mixingangle given by sin θ m = δ ω m . (10)Since the dark ages take place on the order of a hundredmillion years after the Big Bang, and we want oscillationsto be effective on this timescale, an initial guess mightbe that δ ∼ O (10 − ) GeV. An immediate takeaway isthat the mixing is sensitive to exceedingly small effects. In particular, we must ensure that the SM and mirrorhydrogen masses are highly degenerate, | m H − m H (cid:48) | (cid:46) δ ,to avoid the mixing angle being extremely small even in Strictly speaking, H and H (cid:48) are in-vacuum energy eigenstatesonly when δ vanishes. E H and E H (cid:48) are the energies of the non-mixing theory. For comparison, this estimate suggests that δ is about 20 ordersof magnitude smaller than the comparable parameter in the massmixing of neutrinos at MeV energies. 𝑇 𝑅 ∝ 𝑎 −1 𝑇 𝑔 ∝ 𝑎 −2 𝑧 𝑟𝑒𝑐 ~200 ~40 ~20 ~15 𝑧 T e m p e r a t u r e Schematicevolutionof 𝑇 𝑆 Wouthuysen − Fieldeffect
Figure 1. The schematic evolution of the spin temperature and its relation to the radiation and gas temperatures in ΛCDM.During the first part of the dark ages, the SM gas remains thermally coupled to the CMB. After this coupling becomes inefficient,the spin temperature collisionally couples to the gas as it evolves adiabatically, until this coupling becomes inefficient and thespin temperature recouples to the CMB. After stars turn on, the Wouthuysen-Field effect again couples the spin temperatureto the gas temperature, then eventually the stars heat the gas above the CMB temperature. Further detail may be found ine.g. the reviews [86, 89, 90]. In comparison, our model results in super-adiabatic cooling of the gas starting after z ∼
200 andending before z ∼
20, resulting in the spin temperature recoupling to a colder T g . vacuum. Hereafter we adopt E H = E H (cid:48) , which holds ifthe Z symmetry relating SM to mirror fields is exact,since in that case the masses and atomic structures inthe two sectors are identical.The potentials V H and V H (cid:48) quantify the refraction ex-perienced by H and H (cid:48) as they traverse the medium. Thephysics is essentially the same as for a classical wave. Fora hydrogen atom with de Broglie wave number k ≈ m H v ,the index of refraction is n = 1 + (cid:88) i πn i k f i (0) , (11)with the sum calculated over all scattering processes,each process i having density of scatterers n i and elas-tic forward-scattering amplitude f i (0). The velocity inmedium is related to that in vacuum by v = v /n , or v ≈ v (cid:32) − (cid:88) i πn i k f i (0) (cid:33) , (12)from which it follows that the potential due to themedium is V H = E H − E H ≈ − (cid:88) i πn i m H f i (0) (13)to lowest order.The final term in the kinetic equation, the collisionterm i C , receives contributions from collisional processesin both sectors, including H (cid:48) –DM interactions. It has two crucial effects: redistribution of momentum and de-coherence of the H – H (cid:48) system into interaction states. Baryonic cooling is achieved by the cooperation of oscil-lations and collisions. Schematically, a hydrogen atomwith momentum p is brought down to momentum p (cid:48) bythe sequence H ( p ) oscillation −−−−−−→ H (cid:48) ( p ) H (cid:48) –DM −−−−−→ H (cid:48) ( p (cid:48) ) oscillation −−−−−−→ H ( p (cid:48) ) . (14)For the entire sequence to be efficient on a cosmictimescale, in-medium, decoherence-affected oscillationsand heat transfer from H (cid:48) to DM must both be fast rel-ative to the Hubble rate.Under the assumption that the mixing channel is inequilibrium, the number densities and temperatures ofthe hydrogen species satisfy n H = n H (cid:48) and T g ≡ T H = T H (cid:48) , rendering the kinetic treatment superfluous. Theevolution of the gas temperature is simply described (hereas a function of scale factor a ) by Ha dT g da = − HT g + Γ C ( T CMB − T g ) + 23 ˙ Q g , (15) Because H and H (cid:48) have completely distinct sets of (non-gravitational) interactions, all scattering events that change theatom’s momentum also change its coherence. This sort of state-ment is not universally true, though. Neutral-current scatteringof neutrinos, for example, can change a neutrino’s momentumwithout decohering it in flavor space. written in terms of the Compton scattering rate Γ C andthe heating rate ˙ Q g due to H (cid:48) –DM scattering. This for-mula is identical to the one appearing in cooling scenarioswith SM–DM scattering. As in those models, ˙ Q g includesdissipative heating associated with the bulk velocity ofthe gas—in our case the mirror-sector gas—relative toDM.Since our aim is to demonstrate feasibility, we will sim-plify the problem even further and just establish that thedesired hierarchy of timescales (specifically the timescalesof mixing, heat transfer, and Hubble expansion) can berealized. We start with mixing. The equilibration rateof the mixing channel is [91–95]Γ osc ∼ Γ c θ m c / ω m ) , (16)where the total rate of collisions Γ c = Γ H + Γ H (cid:48) is thesum of the scattering rates of H and H (cid:48) . As shown inRef. [95], Eq. (16) emerges from the quantum kineticequation upon assuming that nonequilibrium deviationsof the density matrix decay exponentially. The physicshere can be understood by breaking down the right-handside into three pieces. The appearance of sin θ m sig-nals that equilibration takes longer if the mixing angleis small. The leading Γ c factor captures the intuitionthat a faster decoherence rate entails a faster H (cid:48) produc-tion rate. The term in the denominator demonstratesthat this trend is only valid up to a point: If a quantumstate is measured too quickly (Γ c (cid:29) ω m ), it will neverhave time to develop coherence and will be stuck close toits initial state. This regime of mixing is known as thequantum Zeno limit.The task now is to estimate the various contributionsto Γ c and ∆ V . Working very approximately, the H − H scattering rate over 20 (cid:46) z (cid:46)
200 isΓ H − H ( z ) ∼ n H (cid:104) σv (cid:105) H − H ∼ ( ηn CMB ) (cid:0) πa (cid:1) (cid:114) T g m H ∼ (cid:0) × − GeV (cid:1) (1 + z ) , (17)where η ∼ × − is the cosmic baryon asymmetry, a = 3 × − eV − is the Bohr radius, and n CMB is thenumber density of CMB photons.Rayleigh scattering with CMB photons occurs at a rateΓ H − CMB ∼ n CMB σ T (cid:18) (cid:104) ω (cid:105) CMB ω Ly α (cid:19) ∼ (cid:0) × − GeV (cid:1) (1 + z ) , (18)where σ T ∼ × − eV − is the Thomson cross section, ω Ly α is the Ly α transition frequency, and (cid:104) ω (cid:105) CMB is the There are subtleties pertaining to the accuracy of Eq. (16) nearmaximal mixing θ m ∼ π/
4, but the equation is adequate for ourpurposes. average frequency of a CMB photon. The severe (1 + z ) scaling is a consequence of the CMB background dilutingand redshifting. These interactions are always subdomi-nant at z (cid:46) H − H forward scattering as f H − H (0) ∼ − a , thepotential associated with this process is V H − H ( z ) ∼ πn H a m H ∼ (cid:0) × − GeV (cid:1) (1 + z ) . (19)By the same general formula, but using f H − CMB (0) ∼ α a (cid:18) (cid:104) ω (cid:105) CMB ω Ly α (cid:19) (20)for the H − γ amplitude, we find V H − CMB ∼ − (cid:0) × − GeV (cid:1) (1 + z ) (21)for the potential generated by the CMB.Another possible contribution to V comes from mag-netic fields. Fields in the IGM today are on the order ofa nanogauss, which translates to | V B | ∼ µ B B ∼ × − GeV , (22)a magnitude large enough to take seriously. Considerableuncertainties surround the physical origin of these fields,however. We refer to Ref. [97] for a review of their sta-tus. It is conceivable that present-day magnetic fields arethe products of standard cosmological and astrophysicalprocesses, though even here the development over red-shift is rather uncertain. The most concrete predictionsfind magnetic fields generated during recombination ofsize B ∼ − − − G, and during reionization ofsize B ∼ − − − G [98–106]. For comparison, | V B | (cid:38) | V H − H | at z ∼ B (cid:38) − G, or at z ∼
20 for B (cid:38) − G. We hence neglect magneticfields in our analysis of Γ osc , assuming that they are in-significant for mixing throughout most of the IGM untilafter the universe has reionized. We do note, though, This estimate can be justified from either a classical or a quantumeffective theory. In the former case, we regard a bound electron asan oscillating dipole with natural frequency ω Ly α and dipole mo-ment p = e E / (cid:104) m e (cid:16) ω − ω α (cid:17)(cid:105) , where ω and E are the fre-quency and electric field amplitude associated with the incidentphotons. The Poynting flux radiated along a given direction isproportional to ω p and the incident energy flux is proportionalto E . Hence at low photon energies dσ/d Ω ∼ α a (cid:0) ω/ω Ly α (cid:1) ,motivating Eq. (20). Alternatively, one can write down an effec-tive Lagrangian for photon–hydrogen scattering and estimate thecoefficients using the Bohr radius as the only relevant scale [96],resulting in f (0) ∼ a ( k · v ) , where k µ is the photon momentumand v µ is the hydrogen velocity. that the high sensitivity of H – H (cid:48) mixing to magneticfields makes this an intriguing area for further study.As for photons from astrophysical sources, we do notattempt here to model their evolution. Instead, we showthat it’s reasonable to expect oscillations to be in equilib-rium during reionization, using z = 7 as a representativeredshift. Assuming that there are O (10) ionizing photonsper baryon at reionization, it follows that V H − γ ( z = 7) ∼ − × − GeV . (23)For the scattering rate, we note that the photoionizationcross section is well approximated by σ I ∼ × − cm (cid:16) ω γ . (cid:17) − , (24)which means that σ I ∼ σ T at photon frequencies ω γ near the ionization threshold. This makes photoioniza-tion the dominant contribution to Γ H during the epochof reionization. We findΓ H − γ ( z = 7) ∼ × − GeV . (25)Fig. 2 summarizes the in-medium effects on mixing.From recombination down to reionization, the dominantprocess by far is H – H scattering. During the epoch ofreionization, H – γ scattering takes over as the dominantcontribution to Γ c . Forward scattering on photons, re-gardless of their source, remains subdominant. H (cid:48) – H (cid:48) scattering contributes to Γ c and ∆ V as well. Itis described by the same formulas as H – H scattering butwith the replacement H → H (cid:48) . The conversion of H into H (cid:48) decreases Γ H − H and | V H − H | and increases Γ H (cid:48) − H (cid:48) and | V H (cid:48) − H (cid:48) | . These changes have no net effect on Γ c ,but they do on ∆ V , driving it to zero as n H and n H (cid:48) equilibrate. Feedback of this kind is unimportant for ourtimescale analysis, however.Adopting a phenomenological approach, weparametrize the H (cid:48) –DM momentum-transfer crosssection as¯ σ H (cid:48) − X = (cid:90) d cos θ (1 − cos θ ) dσ H (cid:48) − X d cos θ = σ | (cid:126)v m | n , (26)where (cid:126)v m is the relative velocity of the scattering par-ticles. The heat-transfer rate ˙ Q g appearing in Eq. (15)depends on ¯ σ H (cid:48) − X and has been studied elsewhere in re-lation to models with SM–DM interactions. Using thisparametrization, we approximate the final terms in themixing as Γ H (cid:48) − X ∼ ρ X m X ¯ σ H (cid:48) − X v m (27)and V H (cid:48) − X ∼ ρ X m H m X √ π ¯ σ H (cid:48) − X , (28)where ρ X is the DM energy density. C. Minimal Mixing, Maximal Cooling
For simplicity, our strategy is to focus on H (cid:48) – X inter-actions that do not substantially change the mixing dy-namics at any point ( minimal mixing ) but successfullybring H (cid:48) and X into thermal equilibrium ( maximal cool-ing ). The same strategy was adopted in Ref. [78]. Herewe summarize the main points and provide further elab-oration.This region of parameter space is simple to treat fortwo reasons. First, the redshifts at which mixing be-comes and ceases to be efficient are determined solely bySM parameters and δ . Constraints are straightforwardto apply when the mixing timeline itself does not de-pend on ¯ σ H (cid:48) − X . Second, the requisite DM mass m X canbe approximated by a simple function of the desired gastemperature if H (cid:48) cools to the furthest extent possible.At high redshifts, Γ osc is enhanced by the large scat-tering rate but is suppressed to an even greater extentby the small in-medium mixing angle and the quantumZeno effect. It reaches a peak at | ∆ V | ∼ δ . Then, af-ter the transition to θ m ∼ θ , the mixing rate becomesindependent of δ and falls off as Γ osc ≈ Γ c /
4. One musttake δ (cid:38) × − GeV to ensure that mixing comes intoequilibrium prior to z ∼ osc to exceed H at z = 7—a coarseapproximation of what it takes for n H (cid:48) to track thefalling neutral fraction of SM hydrogen—places a bound δ (cid:38) × − GeV. During the epoch of reionization,a significant hierarchy appears between Γ c and | ∆ V | , asseen in Fig. 2, because ionization photons disproportion-ately contribute to decoherence versus forward scatter-ing.Restricting the mixing dynamics to be independentof H (cid:48) – X interactions translates to an upper bound on¯ σ H (cid:48) − X . We observe that (cid:12)(cid:12)(cid:12)(cid:12) V H (cid:48) − X V H − H (cid:12)(cid:12)(cid:12)(cid:12) > Γ H (cid:48) − X Γ H − H (29)for n ≤ | V H (cid:48) − X | (cid:46) | V H − H | rather than from Γ H (cid:48) − X (cid:46) Γ H − H . The resultingconstraint is ¯ σ H (cid:48) − X ( z = 20) σ H − H (cid:46) . , (30)written it as a fraction of the hard-sphere atomic crosssection σ H − H = 4 πa .Thermalization of H (cid:48) and DM while mixing is in equi-librium leads to T g = T H (cid:48) = T X , the last of these beingthe DM temperature. The idealized best-case coolingscenario—in which both the DM thermal energy and theheating due to bulk relative velocities are neglected—has[34] T g = T g n H + n H (cid:48) n H + n H (cid:48) + n X ∼ T g
11 + m X , (31)
10 50 100 z1. × - × - × - × - H, Γ , V [ GeV ] H Γ H - H | V H - H | Γ H - CMB | V H - CMB | Γ H - γ ( z = )| V H - γ ( z = )| Figure 2. Comparison of rates affecting the mixing dynamics. Solid curves denote contributions to Γ c , dashed curves to ∆ V .The dotted curve is the Hubble rate. Purple curves represent scattering of hydrogen on photons during the epoch of reionization, z ∼ −
9. Since we are not modeling the evolution of the radiation field from astrophysical sources, in estimating these termswe pick z = 7 and assume that there are ∼
10 ionizing photons per baryon. As a further point of comparison, the light blueband marks the range in δ that can account for the EDGES signal, assuming velocity-independent ¯ σ H (cid:48) − X (see Sec. II C). assuming that H (cid:48) and X do not engage in number-changing interactions. ( T g is the gas temperature due toadiabatic cooling alone.) This expression implies that thedesired amount of cooling is achieved for m X ≈ Q g ∼ − ρ X σ m H ( m H + m X ) (cid:18) T g m H (cid:19) n +12 n Γ (cid:0) n (cid:1) √ π T g . (32)Our criterion for achieving maximal cooling of T g is that | ˙ Q g | H − is at least comparable to the thermal energyof the gas. We now consider n = 0 and n = − n = − necessary in the conventional hydrogen-cooling mod-els [33, 37–41] to avoid issues from scattering efficientlyaround recombination. As papers have also often men-tioned n = − n = − n = 0 to show bycomparison how much more freedom exists for the formof H (cid:48) –DM scattering in our scenario.Beginning with n = 0, we note that cooling becomesmore efficient, relative to the Hubble timescale, at higherredshifts. The condition to impose is thus that coolingbecomes inefficient only after mixing has come into equi-librium. To get a sense for the constraints arising fromthis condition, we note that imposing efficient cooling at z (cid:38)
20 entails ¯ σ H (cid:48) − X σ H − H (cid:38) × − . (33)The lower bound is more lenient by a factor of ∼ δ ∼ × − GeV, the largest mixing parameter atwhich n = 0 is viable. (For larger values, DM thermallycouples to the CMB at z (cid:38) n = −
4, cooling is relatively more efficient at lowerredshifts. The requisite condition now is that H (cid:48) and DMthermally equilibrate sometime before z ∼
20. Thus¯ σ H (cid:48) − X ( z = 20) σ H − H (cid:38) × − . (34)Unlike in the previous case, here the upper limit on δ stemming from the mixing timeline only applies to¯ σ H (cid:48) − X ( z = 20) σ H − H (cid:38) × − (35)because cross sections below this threshold are unable totransfer heat efficiently between H (cid:48) and X at z (cid:38) as-suming that m X ≈ , that cooling is maximallyefficient in the sense specified above Eq. (31) , and that H (cid:48) –DM interactions are always subdominant in the mix-ing dynamics. It is notable that n = − n = 0, asone might expect in a model where the cooling is causedby SM–DM scattering. Although the v − m scaling doesmake cooling more efficient at later times, V H (cid:48) − X is alsoenhanced, threatening to push us out of the limit of min-imal mixing. In the end, having m X be comparable to m H means that ¯ σ H (cid:48) − X cannot deviate too much from σ H − H .Relaxing the maximal-cooling assumption potentiallyenlarges the viable parameter space quite significantlybecause m X is no longer anchored to the GeV scale. Twopossibilities present themselves. The first is that H (cid:48) and X still thermally equilibrate but the initial thermal en-ergy of X is not negligible. Then T g ∼ T g
11 + m X + T X
11 + m X , (36)where (3 / T X is the average kinetic energy per DM par-ticle in the baseline scenario without heat exchange be-tween DM and the gas. T X may or may not be an actualtemperature. DM masses much below 2 GeV can be con-sistent with the gas temperature inferred from EDGESif T X is itself approximately equal to that temperature.The mass cannot be made arbitrarily small, however, be-cause it is limited by the effects of DM free streaming onstructure formation.The second possibility is that H (cid:48) and X do not ther-mally equilibrate. Again m X must be below ∼ III. MICROPHYSICAL ORIGINSA. Mirror Matter EFT
While the cosmological analysis of Section II dependsonly on the state hydrogen mixes with, the near-exact degeneracy required demands symmetry-enforced protec-tion. To the tiny degree of splitting we require, all SMparticles contribute to the mass of hydrogen, so we im-pose a Z symmetry which exchanges every SM particlewith a mirror copy charged under a mirror version of theSM gauge group. As a result, the SM and mirror sec-tor spectra contain exactly degenerate hydrogen boundstates.Mixing of hydrogen with anti hydrogen has been con-sidered previously in the context of grand unified theo-ries (GUTs) where baryon number B and lepton number L are no longer accidental global symmetries. As a re-sult, baryon and lepton number may be broken eitherexplicitly or, often, spontaneously, as with the majoron[110]. Since violation by a single unit is strongly con-strained by the requirement of proton metastability, thismotivates study of the violation of baryon and/or leptonnumber by two units, as in hydrogen-antihydrogen mix-ing or neutron-antineutron mixing [111–116]. These maybe constrained by both laboratory tests and cosmologicalobservations [117–119].In the context of mirror models, the mixing of neu-trons with mirror neutrons has seen detailed study andbounds exist from dedicated searches [120–129], but toour knowledge the mixing of hydrogen with mirror hy-drogen has not previously been considered. On generalgrounds one might expect that n − n (cid:48) mixing is alwaysfar more important—not only does it come from a lower-dimension operator, but H – H (cid:48) mixing from a contact op-erator gets an enormous relative penalty from the wave-function overlap of the electron with the proton.However, if our mirror model incorporates a ‘twisted’ B + L (cid:48) and/or B (cid:48) + L symmetry, n − n (cid:48) oscillation isdisallowed and hydrogen-mirror hydrogen mixing can bethe leading connection between the two sectors. We thusconsider an effective theory which is a mirror model withthese symmetries imposed. The choice of sign in B ± L (cid:48) and/or B (cid:48) ± L merely dictateswhether SM hydrogen mixes with mirror hydrogen or mirror an-tihydrogen. In either case, gauging this symmetry in the UVwould require additional heavy fermions to cancel anomalies. Of course the marginal kinetic mixing portal and Higgs portalinteractions are also allowed, but are not compulsory and arenot generated appreciably by the toy UV completion of SectionIII B. A large Higgs portal interaction in the Z -symmetric theorymay violate Higgs coupling measurements [130, 131] unless itis implemented somewhat exotically [132]. The other challengewith introducing these additional couplings is the prospect thatthey will equilibrate the sectors in the early universe [133], butthis can be avoided if the couplings are small enough [134] and/orthe reheating temperature is low enough [133, 135]. It would bean interesting direction to augment this work with a version ofthe twin Higgs mechanism [84] and so connect to the physics ofthe hierarchy problem. We refer to [136] for a recent pedagogicalreview thereof. We note parenthetically that one could introduce a small n − n (cid:48) mixing which would be technically natural as the only source of B + L (cid:48) -breaking. It may be interesting to construct scenarioswhere both mixings occur and n − n (cid:48) mixing is responsible for QCD , hydrogen-mirrorhydrogen mixing begins its life as an 8-fermion operatorwith all the constituent elementary partons. This is adimension-12 operator of the schematic form O partonic ∼ ¯ e (cid:48) e ¯ u (cid:48) u ¯ u (cid:48) u ¯ d (cid:48) d + h.c. , (37)where we give solely the constituent fields and note thatthere are many different spinor contractions possible. Tofind the low-energy mass mixing such partonic operatorsinduce, we must first map these to hadronic operatorssuch as O hadronic ∼ (4 π ) Λ Λ ¯ e (cid:48) Γ e ¯ p (cid:48) Γ p + h.c. , (38)where Γ ∈ { , γ , γ µ , γ µ γ , σ µν , σ µν γ } . We havematched the interpolating operator uud ∼ π Λ p solely using dimensional analysis, with Λ QCD the onlyrelevant scale and 4 π a strong coupling factor. As far aswe are aware it is not known how to calculate the mapfrom these partonic operators to the hadronic operatorsin full detail. Finally, these operators lead to mixing ofa strength δ n,F = (cid:10) H n,F | O hadronic | H (cid:48) n,F (cid:11) δ n,F ∼ (4 π ) Λ Λ n a , (39) δ F ≡ δ ,F ∼ − GeV (cid:18) Λ QCD
250 MeV (cid:19) (cid:18)
260 GeVΛ (cid:19) (40)where n is the principal quantum number, F is the hy-perfine quantum number, and the factors of the Bohrradius a are a contact operator penalty for finding theelectron inside the proton. Since it is a contact opera-tor no mixing occurs for the (cid:96) > F = 1 state.We defer consideration of such scenarios to later work. B. Toy UV Completion
We can write down a toy model of a UV completionwhich gives this mixing by adding leptoquarks with theappropriate quantum numbers. Leptoquarks are bosonscarrying both baryon and lepton number and are in gen-eral among the most well-motivated extensions to the other observed puzzles (e.g. [125]) but we do not consider thispossibility further.
Field SU (3) SU (2) U (1) B + L (cid:48) B (cid:48) + Lω q − − ω (cid:96) −
13 13 ω (cid:48) q (cid:48) − (cid:48) − ω (cid:48) (cid:96) (cid:48) − (cid:48) Table I. A toy UV completion which generates H – H (cid:48) mixingvia the addition of two SM leptoquarks and two mirror lep-toquarks with different B + L (cid:48) charges. The upper two rowshave only SM gauge charges and the lower two rows have onlymirror gauge charges. The global charges allow ω q to interactsolely with pairs of quarks, while ω (cid:96) interacts with a quarkand a lepton. ω q may alternatively be called a ‘diquark’ fromthe perspective of its SM couplings. SM, appearing ubiquitously in grand unified theories asa consequence of unifying quarks and leptons (e.g. [137]).Lighter, TeV-scale leptoquarks are predicted in mod-els ranging from supersymmetric extensions of the SMwhich violate R-parity (e.g. [138–140]) to models of ex-tended technicolor to models where our familiar fermionsare composite (e.g. [141]). In recent years light lepto-quarks have been suggested as sources of various flavoranomalies (e.g. [142]). Our leptoquarks differ from thestandard ones solely by being charged under the twistedglobal symmetries. Technically, this global symmetry as-signment means half of ours might be called ‘diquarks’as their only allowed coupling to SM fermions is to twoquarks, but we’ll continue to use ‘leptoquarks’ as a gen-eral label because their only conserved quantum numbermixes baryon and lepton numbers.Multiple choices of gauge charges and spin are pos-sible, but for simplicity we use pairs of SM and mirrorscalars with the same gauge charges but different chargesunder the global symmetries, as listed in Table I. We’llconsider further adding N ω of each type. We eschew em-bedding them in a particular UV model and introducetheir couplings solely as a proof of principle. We empha-size that including these states does not lead to mixingof other states at appreciable levels—neither of funda-mental states with the photon kinetic mixing portal orthe Higgs portal, nor of other composite states such asneutrons or pions.These scalars allow a mixed quartic coupling L ⊃ λ ijkl ω i † q ω j(cid:96) ω (cid:48) kq ω (cid:48) l † (cid:96) + h.c. (41)where i, j, k, l = 1 ..N ω , and for simplicity we’ll take λ ijkl ≡ Their global charges are also chosen suchthat each SM leptoquark couples either to a B = 2 / , L =0 or B = 1 / , L = 1 fermion current (and the same on the We mention parenthetically that including generic scalar por-tal interactions ∼ | ω | | ω (cid:48) | will allow two-loop diagrams mixingother neutral bound states such as pions or positronium. As a re-sult of suppression from the UV masses, the resulting oscillationtimescales are safely far longer than their lifetimes. qqq e q'q'q' e' ω † q' ω † q ω ℓ ω ℓ' ൗ𝟏 𝟑 ൗ𝟏 𝟑 ൗ ൗ ൗ𝟏 ൗ SM SM'B+L' B'+L
Figure 3. The Feynman diagram generating O partonic in thetoy UV completion of Section III. Particles carrying SM gaugecharges are in blue, while those with mirror gauge charges arein red. Arrows track global charge flow, with green arrowsgiving B + L (cid:48) and orange arrows giving B (cid:48) + L . mirror side), which is necessary to prevent rapid protondecay. Their interactions have the schematic form L ⊃ λ q ω † Aq (cid:15) ABC (cid:0) ¯ d BR u cCR + ¯ q BL iσ q cCL (cid:1) + λ (cid:96) ω † (cid:96) (¯ e cR u R + ¯ q cL iσ (cid:96) L )+ λ q ω (cid:48)† A (cid:48) q (cid:15) A (cid:48) B (cid:48) C (cid:48) (cid:16) ¯ d (cid:48) B (cid:48) R u (cid:48) cC (cid:48) R + ¯ q B (cid:48) L iσ q cC (cid:48) L (cid:17) + λ (cid:96) ω (cid:48)† (cid:96) (¯ e (cid:48) cR u (cid:48) R + ¯ q cL iσ (cid:96) L )+ h.c. (42)where capital Latin letters are used as color indices, wehave left off the species indices for compactness, and wehave mostly followed the notation of [143] (though thefield with these gauge quantum numbers is denoted ‘ ω ’in their work). These interactions allow a tree-level di-agram generating the operator O partonic at low energieswith Λ (cid:39) M ω , as seen in Figure 3. The multiplicity N ω ofthe leptoquarks allows for N ω such diagrams connectingthe sectors, which has the effect of lowering the effectivescale suppressing the higher-dimensional operator for agiven leptoquark mass Λ (cid:39) M ω / √ N ω .In Section II we found that the approximate size of themixing necessary to account for the EDGES anomaly was δ (cid:38) − GeV. Inverting our approximate relationshipbetween the partonic operator and the mixing, and set-ting all the couplings to unity, we have M ω (cid:46) (4 π ) Λ N ω a δ (43) M ω (cid:46)
260 GeV (cid:18) Λ QCD
250 MeV (cid:19) / (cid:112) N ω (44) As our toy UV completion contains new colored states,the LHC imposes constraints on their masses which arein tension with this upper bound for N ω (cid:39)
1. Thereare lower bounds from the LHC on the masses of lep-toquarks ω (cid:96) decaying to a quark and lepton pair [144–146]. These leptoquarks admit couplings to both theleft-handed and right-handed quark and lepton pairs, andthe lower bound on their mass depends on their branch-ing ratio to charged leptons. The limit ranges from M ω (cid:96) (cid:38) M ω (cid:96) (cid:38) O (1)couplings [148, 149], though a precise bound would re-quire a dedicated reinterpretation of those studies. Un-derstanding the bound as a function of both M ω and λ q may reveal slightly more parameter space, as the produc-tion cross-section and δ depend upon these in differentways.Furthermore, with many degenerate or near-degenerate scalars their total differential cross-section todijet pairs may greatly deviate from the Breit-Wignerlineshape. This may result in lowered efficiency for find-ing these signals when searches rely explicitly on fittingthe data to resonance signal shapes, or when estimatingbackgrounds by analyzing sidebands which may havebeen contaminated with signal events. Reinterpretingthose studies to found bounds in the ( M ω , λ q , N ω ) spacemay be an interesting, albeit challenging, exercise.As our interest is solely in providing a proof of con-cept we don’t analyze these possibilities further, andsimply note that the constraint in the simplest case is M ω ≡ (cid:112) M ω (cid:96) M ω q (cid:38) N ω ∼ . At the costof 4( N ω −
1) additional particles, the mixing increasesby a factor of N ω . As for an ultraviolet reason for thisincreased multiplicity, it may naturally result from theleptoquarks carrying an additional quantum number of a(broken) non-Abelian group. In such a case, at weak cou-pling their Yukawa interactions with SM fermions wouldhave to be loop-suppressed, whereby the reduced cou-pling would have them easily evade collider bounds. Em-bedding the scenario into extended technicolor or somesort of SM fermion compositeness might give rise to largesuch Yukawa couplings, but would likely produce a widevariety of such effects, which may be dangerous.2 IV. OTHER ASPECTS OF THE COSMOLOGYAND ASTROPHYSICS
In the foregoing sections we have established that thehydrogen portal has viable parameter space and can besituated within a plausible UV completion. We now turnto several cosmological and astrophysical issues raised bythe scenario, proceeding in roughly chronological order.
A. Mirror Sector Cosmology
The cosmology of mirror sectors has been explored ex-tensively in many directions, and we refer readers to thereviews [80, 150, 151]. Much of this literature breaks the Z symmetry either explicitly or spontaneously–either toset up the requisite dearth of mirror matter, or to al-low some species of mirror matter to be the dark matter.However, we require that the Z symmetry remains very,very good, while still populating only the SM sector anda dark matter sector which communicates only with theunpopulated mirror sector.The simplest option to populate the SM is to keep the Z exact at the level of the theory, and to rely on cosmicvariance giving effectively asymmetric initial conditionsin our Hubble patch. In a model with a pair of indepen-dent inflatons, there are regions of the universe where, bychance, the SM inflaton takes on large field values whilethe mirror inflaton is near the origin of field space. Sucha Hubble patch may then contain primarily SM matterafter reheating. This was first discussed long ago in thecontext of ‘old inflation’, but can be adapted to otherinflationary scenarios [152–155].It is not necessary that mirror matter be entirely ab-sent in the early universe, but precision measurementsof the CMB strongly constrain the energy density in rel-ativistic particles during recombination [156]. For themirror sector temperature this requires T mirror (cid:46) T SM [155], which leads to a large suppression of mirror energydensity ρ ∝ T . While we have taken the initial mirrorenergy density to vanish for simplicity, it would be in-teresting to explore cosmological histories which do havesome early nonzero mirror energy density, either fromreheating or produced via feeble kinetic mixing (see e.g.[131, 133, 134, 150, 151, 157–166] for some related work).The same sort of reasoning also provides the simplestsort of dark matter model to construct, where again cos-mic variance is relied upon. A simple toy example wouldbe to extend both the SM and mirror sectors with anaxion(-like particle). The production of dark matter maytake place through the well-known ‘misalignment mech-anism’ with a large initial displacement or velocity forthe mirror axion field [167–170]. But it’s entirely pos-sible that in our Hubble patch the SM axion field hadan initial position near its minimum, so that SM ax-ions constitute a negligible portion of dark matter. Thephysics of cooling hydrogen from axion dark matter hasrecently been studied in [73, 75, 171–175]. Of course an even wider range of possibilities would come with twoadditional dark sectors —each of which interacts eitherwith the SM or the mirror sector—arranged such thatsolely the mirror dark sector is populated during reheat-ing. This gives the most freedom in choosing the inter-actions between mirror hydrogen and dark matter, butcomes at the cost of minimality.It is in principle possible that some acceptably-small Z -breaking could be responsible for these effective asym-metries. However, such scenarios will be quite con-strained. As an example, if we posit that DM has Z -violating couplings such that it interacts solely with H (cid:48) ,then H (cid:48) – X scattering is forbidden from being elastic.This is simply because the DM legs in a such a scat-tering diagram can be connected to form an irreducibleone-loop contribution to the H (cid:48) mass, which can be esti-mated to be far too large no matter the DM mass.However, inelastic scattering between mirror hydrogenand dark matter does not necessarily induce such a masssplitting. There is then a conceivable scenario with Z violation where mirror hydrogen scatters off of dark mat-ter into another state, whether that’s an excitation ofa composite dark matter particle, another fundamentaldark sector state, or a (de-)excitation of mirror hydrogen.Models where dark matter scatters inelastically with SMparticles have been considered many times, and have arich phenomenology (e.g. [176–185]).Since the mechanism under consideration allows verygeneral sorts of H (cid:48) –DM interactions, as we saw explicitlyin Section II, we eschew studying any explicit realizationand merely offer the above as qualitative guidance forfuture model building. B. Recombination
Hydrogen oscillations only begin at the start of recom-bination, as a considerable abundance of neutral hydro-gen begins to form. Recombination has been preciselymeasured using CMB data and exactingly studied usingthe nonequilibrium theory of atomic transitions and ra-diative transfer. Is H – H (cid:48) mixing significant at the levelof observation?The concern is that the change in n H (by which,as usual, we mean the neutral atomic number density)due to oscillations might alter the course of recombi-nation and the evolution of the visibility function. Asis well known, recombination does not proceed directly It is simple to estimate the rate for free e + p → e (cid:48) + p (cid:48) reac-tions before recombination and find that it could only be cosmo-logically relevant at enormously high temperatures, which theuniverse may never have attained and which in any case are farabove the validity of the theory of Section III. In the late uni-verse, the cross-section for e + p → e (cid:48) + p (cid:48) can be estimated as σ ∼ − cm for a cutoff Λ ∼ s level is counterbalancedby photoionization of another atom. Having H oscillate(perhaps just partially) on the photoionization timescalewould attenuate this bottleneck to some degree. Onthe other hand, because H (cid:48) oscillates back into H , thebottleneck would not be broken through entirely. Thetiming of recombination would still hinge on the redshift-ing of lines away from resonance and the production ofoff-resonance photons from two-photon decay [186, 187].The crucial point, though, is that the timescale formixing is simply too long. The CMB has a finite width∆ z , which affects the magnitude of polarization on largescales [188, 189]. A Gaussian fit to the visibility functionduring recombination gives a last scattering surface cen-tered at z (cid:39) z ∼
90 [156, 190], cor-responding to a cosmic time of few × yrs. For δ in therange we have been focusing on, the oscillation timescalein the dense medium of the early universe exceeds thisduration because of mixing suppression by sin θ m andthe quantum Zeno effect. C. Structure, Stars, and Reionization
Galaxies and stars form during the dark ages and ul-timately bring the era to a close. The full problem isa unique one in which particle oscillations and gravita-tional dynamics are intertwined. In principle, the evolu-tion should be studied with the quantum kinetic equationfor the density matrix in the space of SM and mirror hy-drogen states. We leave detailed calculation to futurework, here only making some qualitative comments interms of classical mixtures. Such a treatment is at leastpartially justified when discussing the evolution of col-lapsing gas clouds, as the densities climb to sufficientlyhigh values that H – H (cid:48) mixing effectively shuts off. Oncethis point is reached, the SM and mirror components ofa gas cloud can be regarded as evolving independently.Fig. 4 illustrates the shutting-off of mixing at high den-sities, showing how the oscillation timescale Γ − com-pares to the gravitational free-fall time t grav and thepresent age of the universe, for three values of δ and fora gas temperature of ∼ K. The free-fall time is t grav = (cid:18) π Gρ (cid:19) ∼ × yrs n / , (45)where ρ is the mass density and n is the number den-sity in units of cm − . For the mixing parameters we Incidentally, similar considerations do not apply to the slowdowncaused by the optical thickness of Ly n lines. As noted in Sec. III,the l > - Time ( yrs ) n ( cm - ) Figure 4. Comparing the oscillation time scale Γ − in a gascloud of density n and temperature T ∼ K (black curves)with the gravitational free-fall time t grav (red) and the presentage of the universe (dotted). The values of δ are 5 × − GeV(thin), 5 × − GeV (medium), and 5 × − GeV (thick). are considering, oscillations evidently become dynami-cally unimportant at densities that are fairly low fromthe standpoint of collapsing gas clouds. For point of ref-erence, the crossing Γ − ∼ t grav corresponds to a Jeansmass on the order of 10 M (cid:12) for δ = 5 × − GeV.As in the analysis of Sec. II, we neglect the growth ofmagnetic fields, which—like gas densities—are capableof suppressing mixing.At the level of linear cosmology, fluids of hydrogen ormirror hydrogen will behave approximately the same asone another, having the same sound speed and Jeansscales. However, significant radiative cooling is necessaryfor the gas to collapse and fragment into star-forming re-gions [191, 192]. The contraction of a pressure-supportedcloud must proceed quickly enough to avoid the qua-sistatic compression regime, where the gas remains inequilibrium and the pressure continually readjusts to sup-port the cloud against collapse. This requires an orderingof timescales H − (cid:38) t grav (cid:38) t cool (46)where H − is the Hubble time at collapse and t cool is thecooling timescale.It is at this stage that the fluids behave differently,as the SM matter has a leg up on cooling as a resultof the small residual free electron fraction left over fromrecombination. Free electrons catalyze the formation ofmolecular hydrogen via H + e − → H − + γH − + H → H + e − . While atomic hydrogen only cools efficiently down to T ∼ K, whereupon Ly α excitations shut off, H and other molecules facilitate cooling to lower temper-atures by means of their rotational and vibrational lev-els [89, 193–195]. The earliest stars form in minihaloes4with mass M ∼ M (cid:12) , where gas is first able tocool and collapse. These haloes have virial temperatures T vir ∼ few × K , indicating the crucial role playedin their development by H [196–198]. To make contactwith Fig. 4, we note that the critical density at whichthe levels of H reach local thermodynamic equilibriumis n ∼ cm − . This is well above the density at which H – H (cid:48) mixing becomes inefficient, consistent with our as-sertion that, by this phase of collapse, gas clouds of H and H (cid:48) can be regarded as evolving separately.As heavier halos form, the situation changes because H is weakly bound and gets collisionally dissociated attemperatures T (cid:38) × K. This erases the SM advan-tage and puts the sectors on equal footing in massivehalos that start with virial temperatures much abovethis threshold. As already mentioned, such halos canonly cool down to T ∼ K through atomic hydro-gen. However, during structure formation, shocks canform in these halos with large enough speed to ionizeatomic hydrogen. Afterwards, recombinations are out-of-equilibrium as the gas behind the shock cools, andthe ionization fraction can be well above the equilibriumvalue as it cools to below T ∼ K [199–201]. Atthis point molecular hydrogen can again form by elec-tron catalysis. However, accretion-induced shocks affectSM and mirror hydrogen in largely the same way, and soprepare both fluids to cool and fragment.Predicting when and which objects form in the mir-ror sector is a task beyond the scope of this study, butwe point to a few ideas that have been addressed else-where (though not in connection to the hydrogen mixingportal). The authors of Refs. [202, 203] studied struc-ture formation in the context of a subdominant mirrorsector which is colder than the SM. Quite interestingly,they show that this leads to a mirror ionization fractionwhich is far lower than in the SM, and so mirror struc-ture formation is modified because the mirror sector haloscannot cool efficiently. Not only does their work providequantitative evidence for the modified mirror structureformation history we argued for above, but importantlyit shows that these qualitative arguments are robust tothe inclusion of a subdominant initial mirror sector den-sity. In particular, it will remain the case that SM starswill form first and SM reionization will occur first. Theyalso demonstrated that in low-mass mirror halos, ratherthan forming stars, this creates the possibility for directcollapse to form the seeds of the supermassive black holesobserved at z ∼ −
7. Rather more generally, the for-mation of these early black hole seeds has been proposedto occur with a general subdominant component of darkmatter having quite strong self-interactions [204, 205], asthis model will produce.In higher-mass mirror halos, shocks from gravitationalin-fall may be strong enough to ionize mirror hydrogen,which may then form mirror H and facilitate efficientcooling [202, 203]. In such halos, evolution will proceedqualitatively similarly to SM halos, so it is natural toexpect the formation of mirror stars. Mirror stars have been considered in Refs. [162, 206–214], among others.They have also seen recent study predicting striking ob-servational signatures [215–217]. In the late universe therelic fraction of baryons trapped in the mirror sectorbecomes a dark component which has self-interactionsand dissipative dynamics. Such a component gives riseto the possibility of larger dark bound structures (e.g.[183, 218–220]) and other non-WIMP-like behavior. Infact Refs. [210, 211] proposed (broken- Z ) mirror hy-drogen atoms as a self-interacting DM candidate to ad-dress the ‘cusp v. core’ problem already two decadesago. We refer to [221] for a recent general review of self-interacting DM and its connections to small scale struc-ture issues, though there has been less study of the effectsof a subdominant self-interacting component than is per-haps warranted.Returning to the SM sector, it is likely significant thatthe total fraction of SM gas to DM is half what it wouldbe in the standard cosmology. How this affects the timingof star formation—whether, for example, the formationof the first stars is delayed because a longer period of timeis needed to accrete cold gas—is difficult to say a prioriand will depend on when mixing comes into equilibriumand when, as a cloud begins to collapse, mixing shuts off.An important piece of physics affecting structure for-mation in both sectors is the relative motion betweenbaryons and DM, which traces back to baryon acousticoscillations at the time of recombination [222]. As pho-tons decouple from the baryonic fluid, the sound speeddrops precipitously to ∼ ∼
30 km/s. Theadvection of baryonic density perturbations across DMpotential wells results in a number of important effects,including suppression of the growth of small-scale struc-ture [223–228]. Streaming velocities are particularly im-portant for models with SM–DM scattering in the post-recombination universe because the bulk relative motionis collisionally dissipated, acting as a heat source for bothbaryons and DM [12, 107]. In our scenario, streaming ve-locities are damped by H (cid:48) – X scattering, but with mixingin equilibrium, the generated heat is partially transferredto the SM gas. Beyond affecting the sky-averaged ther-mal evolution, the dissipation of streaming velocities andthe conveyance of heat from H (cid:48) to H alters fluctuationsover the sky.To recap this subsection so far: A no-shortcuts cos-mological study of the hydrogen-portal scenario wouldaccount for the “freezing-out” of mixing in high-densityregions, the different chemical dynamics and collapsed-object formation taking place in the two sectors, the al-teration to SM galaxy and star formation due to the dilu-tion of the gas density, and the relative motion betweenbaryons and DM.Reionization is downstream of these effects, with pos-sible consequences for its timing and tomography. Thereionization history of the universe remains quite un-certain, both theoretically and observationally. As onemeasure of this uncertainty, [229] studies the constraints5placed on a simple, popular three-parameter effectivemodel of the epoch of reionization by a variety of ob-servations. Very roughly, this leads to a 2 σ uncertaintywindow on the point at which the universe was half reion-ized of z ∼ ∼
10, which is ∼
500 million years wide incosmic time. See also e.g. [230–233] for the effects of avariety of data sets on constraining the timing of reion-ization. Without carefully assessing the various ways inwhich hydrogen mixing feeds into the relevant cosmologyand astrophysics, it is difficult to say how and at whatlevel reionization will be affected.The inverse relationship—how reionization affectsmixing—also deserves closer study. In Sec. II we arguedthat the high rate of photoionization successfully main-tains mixing equilibrium in the IGM as the neutral hy-drogen fraction drops. The actual efficiency with whichmirror hydrogen is reconverted is undoubtedly imperfect,though, and depends both on the details of reionizationitself and on what fraction of mirror hydrogen is pro-tected by the suppression of mixing in high-density re-gions.The incomplete reconversion of mirror hydrogen to SMhydrogen may be related to the long-standing puzzle of‘missing baryons’ in the late universe. For decades, ob-servations had only been able to account for 60-70% ofthe number density of baryons that was measured inthe early universe from BBN and the CMB [234–236].Over the past decade, attention has turned increasinglyto an undetected component of the warm-hot intergalac-tic medium (WHIM) as a potential source. And indeed,in the last two years and due to the combined efforts ofmany groups, observations have finally been able to con-firm such a component [237–241]. However, while thisnew component has been confirmed to exist, the amountdetected thus far does not incontrovertibly resolve thediscrepancy. A recent analysis including these observa-tions concluded that 18 ±
16% of the baryons are stillmissing [238].The implications of these new data toward locating allof the missing baryons have sometimes been interpretedwithout reference to the finite precision of the searches.This is sensible given that—to our knowledge—there hasbeen no ‘alternative hypothesis’ previously put forth. Al-though we do not here attempt to quantify what fractionof mirror hydrogen remains in that sector down to lowredshift, it is clear that, within the hydrogen-portal sce-nario, some baryons should be missing. This scenariothus provides clear motivation for a continued, robustprogram of searches for baryons in the late universe. In-creasing the precision with which the know the late-timeinventory of cosmic baryons may be a useful way to falsifythis proposal.
V. CONCLUSION
In this work we have proposed that hydrogen is cooledduring the dark ages on characteristic timescales t ∼ mil- lion years due a dimension-12 operator generated at en-ergies E ∼ (cid:126) / (10 − seconds) which effectively causeshydrogen to disappear during the dark ages and reap-pear during reionization. The particle physics underly-ing the scenario is conventional, simple, and requires nofine-tuning. The enormous deviations from standard cos-mology appear not to be constrained, but are falsifiable inmultiple ways with upcoming and proposed experiments.Our work takes advantage of a mechanism for connect-ing the SM to a dark sector which has not been previ-ously studied, namely the oscillation of hydrogen intoa mirror state over cosmological timescales. Not onlydoes this mechanism provide a portal for hydrogen to becooled down by dark matter, but it very naturally oper-ates solely during the dark ages. Despite changing themakeup of the universe substantially during that time, itthen naturally reverts these changes during the course ofreionization. After studying the cosmological evolutionof the hydrogen temperature during the dark ages, wehave conducted an initial exploration of the qualitativeeffects of oscillations on the epoch of reionization moregenerally.We have explicitly constructed an EFT realization ofthe necessary mixing in which the necessary features aresymmetry-protected in a mirror model. We have thengiven an example of the lowest-lying states in a UV com-pletion, using states that appear naturally in many well-studied models of physics beyond the standard model. Asthe particular interaction of mirror hydrogen with darkmatter is not crucial for understanding the mechanism,we have taken a phenomenological approach and used asimple parametrization of the interactions.It seems unlikely that this mixing could ever be di-rectly probed in late-universe terrestrial or astrophysicalsettings. In any situation where hydrogen is in a boundstate such as a molecule, or confined in a space by walls ofSM matter, or in a medium dense in SM matter, the po-tentials felt by hydrogen and mirror hydrogen will differ far more than the mixing, | ∆ V | (cid:29) δ , which will heavilysuppress oscillations, θ m (cid:28)
1. This makes cosmologicalsettings the only regime in which the mixing will be ap-preciable. Likely the main avenue of exploring this modelwill be studying further detailed behavior of hydrogen inthe early universe. Understanding the precision cosmol-ogy of this model motivates further study of a varietyof features of which we have only pursued initial explo-rations.Such theory efforts will be rewarded in the near-future,as an abundance of 21 cm data will be available froma variety of experiments. Future measurements of thesky-averaged signal by DARE [54], LEDA [55], PRI Z M[56], SARAS [57], and REACH [58] will be able to con-firm the presence of the anomalous absorption featureand measure its shape in further detail. Other upcomingexperiments such as HERA [59], OVRO-LWA [60], andSKA1-LOW [61] will measure the power spectrum of 21cm fluctuations, which will provide a humongous wealthof information about the dark ages.6Of course, the real smoking gun signal of this mech-anism is that it affects solely neutral hydrogen atoms,so that efforts to probe the epoch of reionization viathe line intensity of other atoms, such as helium [62–65], molecular hydrogen [66] and deuterium [67, 68] willprovide a complementary perspective. Measurements ofthese transitions are challenging, as the abundances ofthese elements are far lower than that of atomic hydro-gen. However, if the anomalously cool spin temperatureof hydrogen is confirmed by the current generation ofreionization experiments, this would immediately becomean important place to look.As mentioned in Section II, the (dis)agreement of be-tween early and late-time measurements of the numberdensity of baryons is another interesting probe of thismodel. To our knowledge, this is the first proposal thatthere should be some fraction of missing baryons in thelate universe. Of course it’s difficult to imagine a positive‘detection’ of a particular fraction of missing baryons,but a higher-precision inventory of the baryons at z (cid:39) wants to producesuch a signal. While empirical evidence will of courserequire further detailed study and await future 21cm ex-periments, it is remarkable how many non-trivial checksthis model satisfies with a quite minimal set of inputingredients. There is indeed a modicum of tension be-tween the natural mass scale for the UV completion, Λ (cid:46) TeV / few and the LHC constraints Λ (cid:38) few × TeV.Given the number of things which go right, as well asthe fact that the effect of interest appears ∼
40 ordersof magnitude below the scale of the UV completion andseemingly by chance the natural value is solely in ∼ H (cid:48) and DM whichhas no interplay with the H − H (cid:48) mixing, including thecase of inelastic H (cid:48) -DM interactions. We have further-more restricted to the case of no initial mirror sectordensity, but allowing a nonzero initial density may wellallow for richer structure formation effects in the mirrorsector.There are furthermore aspects of the cosmological his-tory which we studied solely qualitatively or by compar-ing timescales, which are clear targets for further detailedstudy and computation. These range from understand-ing in detail how superpositions of H − H (cid:48) behave whileclumping, to simulating the structure formation historyin both sectors with modified number densities of vari-ous species, to computing the rates of ionizing radiationand the ensuing flow of H (cid:48) back into SM baryons, which would allow for direct connection to the missing baryonsin the late universe. Understanding in detail the dynam-ics in the mirror sector may reveal the production of earlyblack holes [202], and predicting the spectrum of mirrorstars produced could allow us to connect to spectacularastronomical signatures [215, 216].On the side of particle physics, it is clearly of interestto further understand UV complete scenarios in whichthis mechanism is embedded. This would be useful notjust to generate the mixing operator without relying ona multiplicity of scalars, but also in suggesting DM can-didates, or in finding a natural way for mixing to dependon the hyperfine quantum number. As we’ve mentioned,there are a variety of potential connections to other puz-zles that could be made more explicit, from leptoquarksbeing related to grand unification or flavor anomalies,to supersymmetry helping keep Z violation small. Aparticularly intriguing direction is the recent advent ofa twin Higgs model which does not require Z -breaking[132], which may allow one to connect to the physics ofthe hierarchy problem (see e.g. [136] for a recent intro-duction and review thereof).Clearly, the desire to explore this scenario motivatesa wide variety of directions for more-detailed studyby cosmologists and particle physicists alike. Moregenerally, to the extent that early universe particlecosmologists tend to regard the evolution after BBNas being fixed, it is surprising that this humongouschange in the behavior of the universe during the darkages seems unconstrained. It would be interesting topush on this possibility, both on the theoretical side inexploring the space of allowed modifications and on theobservational side in thinking about new probes of thisera. ACKNOWLEDGEMENTS
The authors thank Samuel Alipour-fard, GuidoD’Amico, Robert McGehee, Paolo Panci, and YimingZhong for comments on a draft of this manuscript. LJthanks Anna Schauer for insights into first-star forma-tion and for suggesting a connection to direct-collapseblack holes. SK thanks Vera Gluscevic for presenting anenlightening seminar on 21cm cosmology at the KITP inDecember 2019.The work of LJ was supported by NSF Grant No.PHY-1914242 and by NASA through the NASA Hub-ble Fellowship grant [1] X.-L. Chen and M. Kamionkowski, Particle decays dur-ing the cosmic dark ages, Phys. Rev. D , 043502(2004), arXiv:astro-ph/0310473.[2] S. R. Furlanetto, S. Oh, and E. Pierpaoli, The Effectsof Dark Matter Decay and Annihilation on the High-Redshift 21 cm Background, Phys. Rev. D , 103502(2006), arXiv:astro-ph/0608385.[3] M. Vald´es, A. Ferrara, M. Mapelli, and E. Ripa-monti, Constraining dark matter through 21-cm obser-vations, Mon. Not. Roy. Astron. Soc. , 245 (2007),arXiv:astro-ph/0701301 [astro-ph].[4] A. V. Belikov and D. Hooper, How dark matter reion-ized the Universe, Phys. Rev. D , 035007 (2009),arXiv:0904.1210 [hep-ph].[5] D. T. Cumberbatch, M. Lattanzi, J. Silk, M. Lattanzi,and J. Silk, Signatures of clumpy dark matter in theglobal 21 cm Background Signal, Phys. Rev. D ,103508 (2010), arXiv:0808.0881 [astro-ph].[6] D. P. Finkbeiner, N. Padmanabhan, and N. Weiner,CMB and 21-cm Signals for Dark Matter with a Long-Lived Excited State, Phys. Rev. D , 063530 (2008),arXiv:0805.3531 [astro-ph].[7] T. R. Slatyer, N. Padmanabhan, and D. P. Finkbeiner,CMB Constraints on WIMP Annihilation: Energy Ab-sorption During the Recombination Epoch, Phys. Rev.D , 043526 (2009), arXiv:0906.1197 [astro-ph.CO].[8] A. Natarajan and D. J. Schwarz, Dark matter annihila-tion and its effect on CMB and Hydrogen 21 cm observa-tions, Phys. Rev. D , 043529 (2009), arXiv:0903.4485[astro-ph.CO].[9] A. Natarajan and D. J. Schwarz, Distinguishing stan-dard reionization from dark matter models, Phys. Rev.D , 123510 (2010), arXiv:1002.4405 [astro-ph.CO].[10] B. Yue and X. Chen, Reionization in the WarmDark Matter Model, Astrophys. J. , 127 (2012),arXiv:1201.3686 [astro-ph.CO].[11] M. Vald´es, C. Evoli, A. Mesinger, A. Ferrara, andN. Yoshida, The nature of dark matter from the globalhigh-redshift H I 21 cm signal, Mon. Not. Roy. Astron.Soc. , 1705 (2013), arXiv:1209.2120 [astro-ph.CO].[12] C. Dvorkin, K. Blum, and M. Kamionkowski, Con-straining Dark Matter-Baryon Scattering with Lin-ear Cosmology, Phys. Rev. D , 023519 (2014),arXiv:1311.2937 [astro-ph.CO].[13] C. Evoli, A. Mesinger, and A. Ferrara, Unveiling the na-ture of dark matter with high redshift 21 cm line exper-iments, JCAP , 024, arXiv:1408.1109 [astro-ph.HE].[14] H. Tashiro, K. Kadota, and J. Silk, Effects of darkmatter-baryon scattering on redshifted 21 cm signals,Phys. Rev. D , 083522 (2014), arXiv:1408.2571 [astro-ph.CO].[15] I. M. Oldengott, D. Boriero, and D. J. Schwarz,Reionization and dark matter decay, JCAP , 054,arXiv:1605.03928 [astro-ph.CO].[16] A. Rudakovskiy and D. Iakubovskyi, Influence of ˜7 keVsterile neutrino dark matter on the process of reioniza-tion, JCAP , 017, arXiv:1604.01341 [astro-ph.CO].[17] L. Lopez-Honorez, O. Mena, S. Palomares-Ruiz, andP. Villanueva-Domingo, Warm dark matter and the ion-ization history of the Universe, Phys. Rev. D , 103539(2017), arXiv:1703.02302 [astro-ph.CO]. [18] R. H. Brandenberger, R. J. Danos, O. F. Hernandez,and G. P. Holder, The 21 cm Signature of Cosmic StringWakes, JCAP , 028, arXiv:1006.2514 [astro-ph.CO].[19] O. F. Hern´andez, Y. Wang, R. Brandenberger, andJ. Fong, Angular 21 cm power spectrum of a scaling dis-tribution of cosmic string wakes, J. Cosmol. Astropart.Phys. (8), 014, arXiv:1104.3337 [astro-ph.CO].[20] H. Tashiro, E. Sabancilar, and T. Vachaspati, Con-straints on superconducting cosmic strings fromearly reionization, Phys. Rev. D , 123535 (2012),arXiv:1204.3643 [astro-ph.CO].[21] M. Pagano and R. Brandenberger, The 21 cm signa-ture of a cosmic string loop, J. Cosmol. Astropart. Phys. (5), 014, arXiv:1201.5695 [astro-ph.CO].[22] M. Ricotti, J. P. Ostriker, and K. J. Mack, Effect ofPrimordial Black Holes on the Cosmic Microwave Back-ground and Cosmological Parameter Estimates, Astro-phys. J. , 829 (2008), arXiv:0709.0524 [astro-ph].[23] K. J. Mack and D. H. Wesley, Primordial black holes inthe Dark Ages: Observational prospects for future 21cmsurveys, (2008), arXiv:0805.1531 [astro-ph].[24] H. Tashiro and N. Sugiyama, The effect of primordialblack holes on 21 cm fluctuations, Mon. Not. Roy. As-tron. Soc. , 3001 (2013), arXiv:1207.6405 [astro-ph.CO].[25] K. Belotsky and A. Kirillov, Primordial black holes withmass 10 − g and reionization of the Universe,JCAP , 041, arXiv:1409.8601 [astro-ph.CO].[26] S. Wyithe, A. Loeb, and P. Geil, Baryonic Acoustic Os-cillations in 21cm Emission: A Probe of Dark Energyout to High Redshifts, Mon. Not. Roy. Astron. Soc. ,1195 (2008), arXiv:0709.2955 [astro-ph].[27] J.-Q. Xia and M. Viel, Early dark energy at high red-shifts: status and perspectives, J. Cosmol. Astropart.Phys. (4), 002, arXiv:0901.0605 [astro-ph.CO].[28] K. Kohri, Y. Oyama, T. Sekiguchi, and T. Takahashi,Elucidating Dark Energy with Future 21 cm Obser-vations at the Epoch of Reionization, JCAP , 024,arXiv:1608.01601 [astro-ph.CO].[29] A. A. Costa, R. C. Landim, B. Wang, and E. Abdalla,Interacting Dark Energy: Possible Explanation for 21-cm Absorption at Cosmic Dawn, Eur. Phys. J. C ,746 (2018), arXiv:1803.06944 [astro-ph.CO].[30] W. Yang, S. Pan, S. Vagnozzi, E. Di Valentino, D. F.Mota, and S. Capozziello, Dawn of the dark: unifieddark sectors and the EDGES Cosmic Dawn 21-cm sig-nal, JCAP , 044, arXiv:1907.05344 [astro-ph.CO].[31] C. Li, X. Ren, M. Khurshudyan, and Y.-F. Cai, Impli-cations of the possible 21-cm line excess at cosmic dawnon dynamics of interacting dark energy, Phys. Lett. B , 135141 (2020), arXiv:1904.02458 [astro-ph.CO].[32] J. D. Bowman, A. E. E. Rogers, R. A. Monsalve, T. J.Mozdzen, and N. Mahesh, An absorption profile centredat 78 megahertz in the sky-averaged spectrum, Nature , 67 (2018), arXiv:1810.05912 [astro-ph.CO].[33] R. Barkana, N. J. Outmezguine, D. Redigolo, andT. Volansky, Strong constraints on light dark matterinterpretation of the EDGES signal, Phys. Rev. D ,103005 (2018), arXiv:1803.03091 [hep-ph].[34] R. Barkana, Possible interaction between baryons anddark-matter particles revealed by the first stars, Nature , 71 (2018), arXiv:1803.06698 [astro-ph.CO].[35] J. B. Mu˜noz and A. Loeb, A small amount of mini-charged dark matter could cool the baryons in the earlyUniverse, Nature , 684 (2018), arXiv:1802.10094[astro-ph.CO].[36] L.-B. Jia, Dark photon portal dark matter with the21-cm anomaly, Eur. Phys. J. C , 80 (2019),arXiv:1804.07934 [hep-ph].[37] H. Liu, N. J. Outmezguine, D. Redigolo, and T. Volan-sky, Reviving Millicharged Dark Matter for 21-cm Cosmology, Phys. Rev. D , 123011 (2019),arXiv:1908.06986 [hep-ph].[38] A. Berlin, D. Hooper, G. Krnjaic, and S. D. McDer-mott, Severely Constraining Dark Matter Interpreta-tions of the 21-cm Anomaly, Phys. Rev. Lett. ,011102 (2018), arXiv:1803.02804 [hep-ph].[39] T. R. Slatyer and C.-L. Wu, Early-Universe constraintson dark matter-baryon scattering and their implicationsfor a global 21 cm signal, Phys. Rev. D , 023013(2018), arXiv:1803.09734 [astro-ph.CO].[40] S. Fraser et al. , The EDGES 21 cm Anomaly and Prop-erties of Dark Matter, Phys. Lett. B , 159 (2018),arXiv:1803.03245 [hep-ph].[41] E. D. Kovetz, V. Poulin, V. Gluscevic, K. K. Boddy,R. Barkana, and M. Kamionkowski, Tighter limits ondark matter explanations of the anomalous EDGES21 cm signal, Phys. Rev. D , 103529 (2018),arXiv:1807.11482 [astro-ph.CO].[42] J. Mirocha and S. R. Furlanetto, What doesthe first highly redshifted 21-cm detection tellus about early galaxies?, Monthly Notices ofthe Royal Astronomical Society , 1980(2018), https://academic.oup.com/mnras/article-pdf/483/2/1980/27140778/sty3260.pdf.[43] R. Jana, B. B. Nath, and P. L. Biermann, Radio back-ground and IGM heating due to Pop III supernova ex-plosions, Mon. Not. Roy. Astron. Soc. , 5329 (2019),arXiv:1812.07404 [astro-ph.HE].[44] P. Sharma, Astrophysical radio background cannot ex-plain the EDGES 21-cm signal: constraints from coolingof non-thermal electrons, Mon. Not. Roy. Astron. Soc. , L6 (2018), arXiv:1804.05843 [astro-ph.HE].[45] A. Ewall-Wice, T.-C. Chang, J. Lazio, O. Dore, M. Seif-fert, and R. Monsalve, Modeling the Radio Backgroundfrom the First Black Holes at Cosmic Dawn: Implica-tions for the 21 cm Absorption Amplitude, Astrophys.J. , 63 (2018), arXiv:1803.01815 [astro-ph.CO].[46] A. Ewall-Wice, T.-C. Chang, and T. J. W. Lazio, TheRadio Scream from Black Holes at Cosmic Dawn: ASemi-Analytic Model for the Impact of Radio LoudBlack-Holes on the 21 cm Global Signal, Mon. Not. Roy.Astron. Soc. , 6086 (2020), arXiv:1903.06788 [astro-ph.GA].[47] R. Hills, G. Kulkarni, P. D. Meerburg, and E. Puchwein,Concerns about modelling of the EDGES data, Nature , E32 (2018), arXiv:1805.01421 [astro-ph.CO].[48] J. D. Bowman, A. E. E. Rogers, R. A. Monsalve, T. J.Mozdzen, and N. Mahesh, Reply to Hills et al., Nature , E35 (2018).[49] R. F. Bradley, K. Tauscher, D. Rapetti, and J. O. Burns,A Ground Plane Artifact that Induces an AbsorptionProfile in Averaged Spectra from Global 21 cm Measure-ments, with Possible Application to EDGES, Astrophys.J. , 153 (2019), arXiv:1810.09015 [astro-ph.IM]. [50] S. Singh and R. Subrahmanyan, The Redshifted 21 cmSignal in the EDGES Low-band Spectrum, Astrophys.J. , 26 (2019), arXiv:1903.04540 [astro-ph.CO].[51] K. Tauscher, D. Rapetti, and J. O. Burns, Formulatingand Critically Examining the Assumptions of Global 21cm Signal Analyses: How to Avoid the False TroughsThat Can Appear in Single-spectrum Fits, Astrophys.J. , 132 (2020), arXiv:2005.00034 [astro-ph.CO].[52] M. Spinelli, G. Bernardi, and M. G. Santos, On thecontamination of the global 21-cm signal from polar-ized foregrounds, Mon. Not. Roy. Astron. Soc. , 4007(2019), arXiv:1908.05303 [astro-ph.CO].[53] P. H. Sims and J. C. Pober, Testing for calibration sys-tematics in the EDGES low-band data using Bayesianmodel selection, Mon. Not. Roy. Astron. Soc. , 22(2020), arXiv:1910.03165 [astro-ph.CO].[54] J. O. Burns, J. Lazio, S. Bale, J. Bowman, R. Bradley,C. Carilli, S. Furlanetto, G. Harker, A. Loeb, andJ. Pritchard, Probing the first stars and black holes inthe early Universe with the Dark Ages Radio Explorer(DARE), Advances in Space Research , 433 (2012),arXiv:1106.5194 [astro-ph.CO].[55] D. C. Price et al. , Design and characterization of theLarge-aperture Experiment to Detect the Dark Age(LEDA) radiometer systems, Mon. Not. Roy. Astron.Soc. , 4193 (2018), arXiv:1709.09313 [astro-ph.IM].[56] L. Philip et al. , Probing Radio Intensity at High-Zfrom Marion: 2017 Instrument, Journal of AstronomicalInstrumentation , 1950004 (2019), arXiv:1806.09531[astro-ph.IM].[57] S. Singh, R. Subrahmanyan, N. U. Shankar, M. S. Rao,B. S. Girish, A. Raghunathan, R. Somashekar, and K. S.Srivani, SARAS 2: a spectral radiometer for probingcosmic dawn and the epoch of reionization through de-tection of the global 21-cm signal, Experimental Astron-omy , 269 (2018), arXiv:1710.01101 [astro-ph.IM].[58] E. de Lera Acedo, Reach: Radio experiment for theanalysis of cosmic hydrogen, in (2019) pp. 0626–0629.[59] A. Parsons et al. , A Roadmap for Astrophysics and Cos-mology with High-Redshift 21 cm Intensity Mapping, in Bulletin of the American Astronomical Society , Vol. 51(2019) p. 241, arXiv:1907.06440 [astro-ph.IM].[60] M. W. Eastwood et al. , The 21 cm Power Spectrum fromthe Cosmic Dawn: First Results from the OVRO-LWA,Astron. J. , 84 (2019), arXiv:1906.08943 [astro-ph.CO].[61] G. Mellema et al. , Reionization and the Cosmic Dawnwith the Square Kilometre Array, Exper. Astron. ,235 (2013), arXiv:1210.0197 [astro-ph.CO].[62] E. Visbal, Z. Haiman, and G. L. Bryan, Looking forPopulation III stars with He II line intensity map-ping, Mon. Not. Roy. Astron. Soc. , 2506 (2015),arXiv:1501.03177 [astro-ph.CO].[63] J. S. Bagla and A. Loeb, The hyperfine transition of3He+ as a probe of the intergalactic medium, arXiv e-prints , arXiv:0905.1698 (2009), arXiv:0905.1698 [astro-ph.CO].[64] M. McQuinn and E. R. Switzer, Redshifted intergalacticHe+3 8.7 GHz hyperfine absorption, Phys. Rev. D ,063010 (2009), arXiv:0905.1715 [astro-ph.CO].[65] S. Khullar, Q. Ma, P. Busch, B. Ciardi, M. B.Eide, and K. Kakiichi, Probing the high-z IGM with the hyperfine transition of 3He+, MonthlyNotices of the Royal Astronomical Society ,572 (2020), https://academic.oup.com/mnras/article-pdf/497/1/572/33527980/staa1951.pdf.[66] Y. Gong, A. Cooray, and M. G. Santos, Probingthe Pre-reionization Epoch with Molecular HydrogenIntensity Mapping, Astrophys. J. , 130 (2013),arXiv:1212.2964 [astro-ph.CO].[67] D. N. Kosenko and A. V. Ivanchik, The influence ofbaryon-photon ratio on 21 and 92 cm brightness tem-perature, Journal of Physics: Conference Series ,012011 (2018).[68] K. Sigurdson and S. R. Furlanetto, Measuring the Pri-mordial Deuterium Abundance during the Cosmic DarkAges, Phys. Rev. Lett. , 091301 (2006), arXiv:astro-ph/0505173 [astro-ph].[69] E. D. Kovetz et al. , Line-Intensity Mapping: 2017 Sta-tus Report, (2017), arXiv:1709.09066 [astro-ph.CO].[70] E. D. Kovetz et al. , Astrophysics and Cosmologywith Line-Intensity Mapping, (2019), arXiv:1903.04496[astro-ph.CO].[71] T.-C. Chang et al. , Tomography of the Cosmic Dawnand Reionization Eras with Multiple Tracers, (2019),arXiv:1903.11744 [astro-ph.CO].[72] A. Liu and J. R. Shaw, Data Analysis for Precision 21cm Cosmology, Publ. Astron. Soc. Pac. , 062001(2020), arXiv:1907.08211 [astro-ph.IM].[73] T. Moroi, K. Nakayama, and Y. Tang, Axion-photonconversion and effects on 21 cm observation, Phys. Lett.B , 301 (2018), arXiv:1804.10378 [hep-ph].[74] M. Pospelov, J. Pradler, J. T. Ruderman, and A. Ur-bano, Room for New Physics in the Rayleigh-Jeans Tailof the Cosmic Microwave Background, Phys. Rev. Lett. , 031103 (2018), arXiv:1803.07048 [hep-ph].[75] K. Choi, H. Seong, and S. Yun, Axion-photon-dark pho-ton oscillation and its implication for 21 cm observation,Phys. Rev. D , 075024 (2020), arXiv:1911.00532[hep-ph].[76] R. Brandenberger, B. Cyr, and T. Schaeffer, On thePossible Enhancement of the Global 21-cm Signal atReionization from the Decay of Cosmic String Cusps,JCAP , 020, arXiv:1810.03219 [astro-ph.CO].[77] R. Brandenberger, B. Cyr, and R. Shi, Constraintson Superconducting Cosmic Strings from the Global21-cm Signal before Reionization, JCAP , 009,arXiv:1902.08282 [astro-ph.CO].[78] L. Johns and S. Koren, Hydrogen mixing as a novelmechanism for colder baryons in 21 cm cosmology,(2020).[79] T. Lee and C.-N. Yang, Question of Parity Conservationin Weak Interactions, Phys. Rev. , 254 (1956).[80] L. Okun, Mirror particles and mirror matter: 50 yearsof speculations and search, Phys. Usp. , 380 (2007),arXiv:hep-ph/0606202.[81] S. Blinnikov and M. Khlopov, On Possible Effects of’Mirror’ Particles, Sov. J. Nucl. Phys. , 472 (1982).[82] D. J. Gross, J. A. Harvey, E. J. Martinec, and R. Rohm,The Heterotic String, Phys. Rev. Lett. , 502 (1985).[83] R. Foot, H. Lew, and R. Volkas, A Model with funda-mental improper space-time symmetries, Phys. Lett. B , 67 (1991).[84] Z. Chacko, H.-S. Goh, and R. Harnik, The TwinHiggs: Natural electroweak breaking from mirror sym-metry, Phys. Rev. Lett. , 231802 (2006), arXiv:hep- ph/0506256.[85] D. McKeen, M. Pospelov, and N. Raj, Hydrogen portalto exotic radioactivity, Phys. Rev. Lett. , 231803(2020).[86] J. R. Pritchard and A. Loeb, 21 cm cosmology in the21st century, Reports on Progress in Physics , 086901(2012).[87] G. B. Field, Excitation of the hydrogen 21-cm line, Pro-ceedings of the IRE , 240 (1958).[88] S. A. Wouthuysen, On the excitation mechanism of the21-cm (radio-frequency) interstellar hydrogen emissionline., Astron. J. , 31 (1952).[89] R. Barkana and A. Loeb, In the beginning: the firstsources of light and the reionization of the universe,Phys. Rept. , 125 (2001), arXiv:astro-ph/0010468[astro-ph].[90] A. Loeb, A. Ferrara, and R. S. Ellis, First light in theuniverse (Springer, 2008).[91] K. Kainulainen, Light singlet neutrinos and the primor-dial nucleosynthesis, Physics Letters B , 191 (1990).[92] J. M. Cline, Constraints on almost-dirac neutrinos fromneutrino-antineutrino oscillations, Phys. Rev. Lett. ,3137 (1992).[93] S. Dodelson and L. M. Widrow, Sterile neutrinos as darkmatter, Phys. Rev. Lett. , 17 (1994).[94] K. S. M. Lee, R. R. Volkas, and Y. Y. Y. Wong, Furtherstudies on relic neutrino asymmetry generation. ii. a rig-orous treatment of repopulation in the adiabatic limit,Phys. Rev. D , 093025 (2000).[95] L. Johns, Derivation of the sterile neutrino boltzmannequation from quantum kinetics, Phys. Rev. D ,083536 (2019).[96] D. B. Kaplan, Five lectures on effective field theory(2005) arXiv:nucl-th/0510023.[97] K. Subramanian, From primordial seed magneticfields to the galactic dynamo, Galaxies , 47 (2019),arXiv:1903.03744 [astro-ph.CO].[98] R. Gopal and S. K. Sethi, Generation of mag-netic field in the pre-recombination era, MonthlyNotices of the Royal Astronomical Society ,521 (2005), https://academic.oup.com/mnras/article-pdf/363/2/521/3912327/363-2-521.pdf.[99] S. Matarrese, S. Mollerach, A. Notari, and A. Riotto,Large-scale magnetic fields from density perturbations,Phys. Rev. D , 043502 (2005).[100] R. M. Kulsrud, R. Cen, J. P. Ostriker, and D. Ryu,The protogalactic origin for cosmic magnetic fields, TheAstrophysical Journal , 481 (1997).[101] N. Y. Gnedin, A. Ferrara, and E. G. Zweibel, Genera-tion of the primordial magnetic fields during cosmolog-ical reionization, The Astrophysical Journal , 505(2000).[102] K. Subramanian, D. Narasimha, and S. M. Chitre, Ther-mal generation of cosmological seed magnetic fields inionization fronts, Mon. Not. Roy. Astron. Soc. , L15(1994).[103] K. Takahashi, K. Ichiki, H. Ohno, and H. Hanayama,Magnetic field generation from cosmological perturba-tions, Phys. Rev. Lett. , 121301 (2005).[104] T. Kobayashi, R. Maartens, T. Shiromizu, and K. Taka-hashi, Cosmological magnetic fields from nonlinear ef-fects, Phys. Rev. D , 103501 (2007).[105] J.-B. Durrive, H. Tashiro, M. Langer, and N. Sugiyama,Mean energy density of photogenerated magnetic fields throughout the Epoch of Reionization, MonthlyNotices of the Royal Astronomical Society ,1649 (2017), https://academic.oup.com/mnras/article-pdf/472/2/1649/19917665/stx2007.pdf.[106] J.-B. Durrive and M. Langer, Intergalactic magneto-genesis at Cosmic Dawn by photoionization, MonthlyNotices of the Royal Astronomical Society ,345 (2015), https://academic.oup.com/mnras/article-pdf/453/1/345/4913470/stv1578.pdf.[107] J. B. Mu˜noz, E. D. Kovetz, and Y. Ali-Ha¨ımoud, Heat-ing of Baryons due to Scattering with Dark Matter Dur-ing the Dark Ages, Phys. Rev. D , 083528 (2015),arXiv:1509.00029 [astro-ph.CO].[108] J. B. Mu˜noz and A. Loeb, Constraints on DarkMatter-Baryon Scattering from the Temperature Evo-lution of the Intergalactic Medium, JCAP , 043,arXiv:1708.08923 [astro-ph.CO].[109] G. Ballesteros, M. A. Garcia, and M. Pierre, Howwarm are non-thermal relics? Lyman- α bounds on out-of-equilibrium dark matter, (2020), arXiv:2011.13458[hep-ph].[110] Y. Chikashige, R. N. Mohapatra, and R. Peccei, AreThere Real Goldstone Bosons Associated with BrokenLepton Number?, Phys. Lett. B , 265 (1981).[111] V. A. Kuz’min, CP-noninvariance and baryon asymme-try of the universe., Soviet Journal of Experimental andTheoretical Physics Letters , 228 (1970).[112] G. Feinberg, M. Goldhaber, and G. Steigman, Multi-plicative Baryon Number Conservation and the Oscilla-tion of Hydrogen Into Anti-hydrogen, Phys. Rev. D ,1602 (1978).[113] S. Misra and U. Sarkar, n ¯ n Oscillation, H ¯ H Oscillationand the Double Proton Decay: Are They Suppressed byWave Function Effects?, Phys. Rev. D , 249 (1983).[114] L. Arnellos and W. J. Marciano, Hydrogen - Anti-hydrogen Oscillations, Double Proton Decay and GrandUnified Theories, Phys. Rev. Lett. , 1708 (1982).[115] R. N. Mohapatra and G. Senjanovic, Hydrogen - Anti-hydrogen Oscillations and Spontaneously Broken Global B − L Symmetry, Phys. Rev. Lett. , 7 (1982).[116] W. E. Caswell, J. Milutinovic, and G. Senjanovic, Mat-ter - Antimatter Transition Operators: A Manual forModeling, Phys. Lett. B , 373 (1983).[117] R. Mohapatra, Neutron-Anti-Neutron Oscillation: The-ory and Phenomenology, J. Phys. G , 104006 (2009),arXiv:0902.0834 [hep-ph].[118] I. Phillips, D.G. et al. , Neutron-Antineutron Oscilla-tions: Theoretical Status and Experimental Prospects,Phys. Rept. , 1 (2016), arXiv:1410.1100 [hep-ex].[119] Y. Grossman, W. H. Ng, and S. Ray, Revisiting thebounds on hydrogen-antihydrogen oscillations from dif-fuse γ -ray surveys, Phys. Rev. D , 035020 (2018),arXiv:1806.08233 [hep-ph].[120] Z. Berezhiani and L. Bento, Neutron - mirror neutronoscillations: How fast might they be?, Phys. Rev. Lett. , 081801 (2006), arXiv:hep-ph/0507031.[121] Z. Berezhiani and L. Bento, Fast neutron: Mirror neu-tron oscillation and ultra high energy cosmic rays, Phys.Lett. B , 253 (2006), arXiv:hep-ph/0602227.[122] Z. Berezhiani, More about neutron - mirror neu-tron oscillation, Eur. Phys. J. C , 421 (2009),arXiv:0804.2088 [hep-ph].[123] Z. Berezhiani, M. Frost, Y. Kamyshkov, B. Rybolt, andL. Varriano, Neutron Disappearance and Regeneration from Mirror State, Phys. Rev. D , 035039 (2017),arXiv:1703.06735 [hep-ex].[124] Z. Berezhiani, R. Biondi, P. Geltenbort, I. Kras-noshchekova, V. Varlamov, A. Vassiljev, andO. Zherebtsov, New experimental limits on neu-tron - mirror neutron oscillations in the presence ofmirror magnetic field, Eur. Phys. J. C , 717 (2018),arXiv:1712.05761 [hep-ex].[125] Z. Berezhiani, Neutron lifetime puzzle and neu-tron–mirror neutron oscillation, Eur. Phys. J. C , 484(2019), arXiv:1807.07906 [hep-ph].[126] G. Ban et al. , A Direct experimental limit on neutron:Mirror neutron oscillations, Phys. Rev. Lett. , 161603(2007), arXiv:0705.2336 [nucl-ex].[127] I. Altarev et al. , Neutron to Mirror-Neutron Oscillationsin the Presence of Mirror Magnetic Fields, Phys. Rev.D , 032003 (2009), arXiv:0905.4208 [nucl-ex].[128] A. Serebrov et al. , Experimental search for neu-tron: Mirror neutron oscillations using storage ofultracold neutrons, Phys. Lett. B , 181 (2008),arXiv:0706.3600 [nucl-ex].[129] R. N. Mohapatra and S. Nussinov, Constraints on Mir-ror Models of Dark Matter from Observable Neutron-Mirror Neutron Oscillation, Phys. Lett. B , 22(2018), arXiv:1709.01637 [hep-ph].[130] G. Burdman, Z. Chacko, R. Harnik, L. de Lima, andC. B. Verhaaren, Colorless Top Partners, a 125 GeVHiggs, and the Limits on Naturalness, Phys. Rev. D ,055007 (2015), arXiv:1411.3310 [hep-ph].[131] N. Craig, A. Katz, M. Strassler, and R. Sundrum,Naturalness in the Dark at the LHC, JHEP , 105,arXiv:1501.05310 [hep-ph].[132] C. Cs´aki, C.-S. Guan, T. Ma, and J. Shu, Twin Higgswith Exact Z , (2019), arXiv:1910.14085 [hep-ph].[133] N. Craig, S. Koren, and T. Trott, CosmologicalSignals of a Mirror Twin Higgs, JHEP , 038,arXiv:1611.07977 [hep-ph].[134] S. Koren and R. McGehee, Freezing-in twin dark mat-ter, Phys. Rev. D , 055024 (2020), arXiv:1908.03559[hep-ph].[135] Z. Chacko, N. Craig, P. J. Fox, and R. Harnik, Cosmol-ogy in Mirror Twin Higgs and Neutrino Masses, JHEP , 023, arXiv:1611.07975 [hep-ph].[136] S. Koren, The Hierarchy Problem: From the Fun-damentals to the Frontiers, PhD thesis (2020),arXiv:2009.11870 [hep-ph].[137] P. H. Frampton, Light leptoquarks as possible signatureof strong electroweak unification, Mod. Phys. Lett. A ,559 (1992).[138] L. J. Hall and M. Suzuki, Explicit R-Parity Breaking inSupersymmetric Models, Nucl. Phys. B , 419 (1984).[139] F. Zwirner, Observable Delta B=2 Transitions WithoutNucleon Decay in a Minimal Supersymmetric Extensionof the Standard Model, Phys. Lett. B , 103 (1983).[140] S. Dawson, R-Parity Breaking in Supersymmetric The-ories, Nucl. Phys. B , 297 (1985).[141] B. Schrempp and F. Schrempp, Light Leptoquarks,Phys. Lett. B , 101 (1985).[142] B. Gripaios, M. Nardecchia, and S. Renner, Compositeleptoquarks and anomalies in B -meson decays, JHEP , 006, arXiv:1412.1791 [hep-ph].[143] J. de Blas, J. Criado, M. Perez-Victoria, and J. Santi-ago, Effective description of general extensions of theStandard Model: the complete tree-level dictionary, JHEP , 109, arXiv:1711.10391 [hep-ph].[144] G. Aad et al. (ATLAS), Search for pairs of scalar lepto-quarks decaying into quarks and electrons or muons in √ s = 13 TeV pp collisions with the ATLAS detector,(2020), arXiv:2006.05872 [hep-ex].[145] A. M. Sirunyan et al. (CMS), Search for pair productionof first-generation scalar leptoquarks at √ s = 13 TeV,Phys. Rev. D , 052002 (2019), arXiv:1811.01197 [hep-ex].[146] M. Aaboud et al. (ATLAS), Searches for scalar lep-toquarks and differential cross-section measurementsin dilepton-dijet events in proton-proton collisions ata centre-of-mass energy of √ s = 13 TeV with theATLAS experiment, Eur. Phys. J. C , 733 (2019),arXiv:1902.00377 [hep-ex].[147] A. Greljo and N. Selimovic, Lepton-Quark Fusion atHadron Colliders, precisely, (2020), arXiv:2012.02092[hep-ph].[148] G. Aad et al. (ATLAS), Search for new resonances inmass distributions of jet pairs using 139 fb − of pp colli-sions at √ s = 13 TeV with the ATLAS detector, JHEP , 145, arXiv:1910.08447 [hep-ex].[149] A. M. Sirunyan et al. (CMS), Search for narrowand broad dijet resonances in proton-proton collisionsat √ s = 13 TeV and constraints on dark mattermediators and other new particles, JHEP , 130,arXiv:1806.00843 [hep-ex].[150] P. Ciarcelluti, Cosmology with mirror dark matter,Int. J. Mod. Phys. D , 2151 (2010), arXiv:1102.5530[astro-ph.CO].[151] R. Foot, Mirror dark matter: Cosmology, galaxy struc-ture and direct detection, Int. J. Mod. Phys. A ,1430013 (2014), arXiv:1401.3965 [astro-ph.CO].[152] E. W. Kolb, D. Seckel, and M. S. Turner, The ShadowWorld, Nature , 415 (1985).[153] H. Hodges, Mirror baryons as the dark matter, Phys.Rev. D , 456 (1993).[154] V. Berezinsky and A. Vilenkin, Ultrahigh-energy neutri-nos from hidden sector topological defects, Phys. Rev.D , 083512 (2000), arXiv:hep-ph/9908257.[155] J.-S. Roux and J. M. Cline, Constraining galactic struc-tures of mirror dark matter, Phys. Rev. D , 063518(2020), arXiv:2001.11504 [astro-ph.CO].[156] N. Aghanim et al. (Planck), Planck 2018 results. VI.Cosmological parameters, Astron. Astrophys. , A6(2020), arXiv:1807.06209 [astro-ph.CO].[157] M. Khlopov, G. Beskin, N. Bochkarev, L. Pustylnik, andS. Pustylnik, Observational Physics of Mirror World,Sov. Astron. , 21 (1991).[158] Z. Berezhiani, D. Comelli, and F. L. Villante, The Earlymirror universe: Inflation, baryogenesis, nucleosynthe-sis and dark matter, Phys. Lett. B , 362 (2001),arXiv:hep-ph/0008105.[159] Z. Berezhiani, L. Gianfagna, and M. Giannotti, StrongCP problem and mirror world: The Weinberg-Wilczekaxion revisited, Phys. Lett. B , 286 (2001),arXiv:hep-ph/0009290.[160] Z. Berezhiani, P. Ciarcelluti, D. Comelli, and F. L.Villante, Structure formation with mirror dark matter:CMB and LSS, Int. J. Mod. Phys. D , 107 (2005),arXiv:astro-ph/0312605.[161] P. Ciarcelluti, Cosmology of the mirror universe , Otherthesis (2003), arXiv:astro-ph/0312607.[162] A. Ignatiev and R. Volkas, Mirror dark matter and large scale structure, Phys. Rev. D , 023518 (2003),arXiv:hep-ph/0304260.[163] P. Ciarcelluti, Cosmology with mirror dark matter. 1.Linear evolution of perturbations, Int. J. Mod. Phys. D , 187 (2005), arXiv:astro-ph/0409630.[164] P. Ciarcelluti, Cosmology with mirror dark matter. 2.Cosmic microwave background and large scale struc-ture, Int. J. Mod. Phys. D , 223 (2005), arXiv:astro-ph/0409633.[165] P. Ciarcelluti and R. Foot, Early Universe cosmologyin the light of the mirror dark matter interpretation ofthe DAMA/Libra signal, Phys. Lett. B , 278 (2009),arXiv:0809.4438 [astro-ph].[166] R. Foot, Mirror dark matter cosmology - predictions for N eff [ CMB ] and N eff [ BBN ], Phys. Lett. B , 238(2012), arXiv:1111.6366 [astro-ph.CO].[167] M. Dine and W. Fischler, The Not So Harmless Axion,Phys. Lett. B , 137 (1983).[168] L. Abbott and P. Sikivie, A Cosmological Bound on theInvisible Axion, Phys. Lett. B , 133 (1983).[169] J. Preskill, M. B. Wise, and F. Wilczek, Cosmology ofthe Invisible Axion, Phys. Lett. B , 127 (1983).[170] R. T. Co, L. J. Hall, and K. Harigaya, Axion KineticMisalignment Mechanism, Phys. Rev. Lett. , 251802(2020), arXiv:1910.14152 [hep-ph].[171] N. Houston, C. Li, T. Li, Q. Yang, and X. Zhang, Natu-ral Explanation for 21 cm Absorption Signals via Axion-Induced Cooling, Phys. Rev. Lett. , 111301 (2018),arXiv:1805.04426 [hep-ph].[172] C. Li, N. Houston, T. Li, Q. Yang, and X. Zhang,A detailed exploration of the EDGES 21 cm ab-sorption anomaly and axion-induced cooling, (2018),arXiv:1812.03931 [hep-ph].[173] P. Sikivie, Axion dark matter and the 21-cm signal,Phys. Dark Univ. , 100289 (2019), arXiv:1805.05577[astro-ph.CO].[174] K. Lawson and A. Zhitnitsky, The 21 cm absorption lineand the axion quark nugget dark matter model, Phys.Dark Univ. , 2019 (2018), arXiv:1804.07340[hep-ph].[175] G. Lambiase and S. Mohanty, Hydrogen spin oscillationsin a background of axions and the 21-cm brightness tem-perature, Mon. Not. Roy. Astron. Soc. , 5961 (2020),arXiv:1804.05318 [hep-ph].[176] D. Tucker-Smith and N. Weiner, Inelastic dark matter,Phys. Rev. D , 043502 (2001), arXiv:hep-ph/0101138.[177] D. P. Finkbeiner and N. Weiner, Exciting Dark Matterand the INTEGRAL/SPI 511 keV signal, Phys. Rev. D , 083519 (2007), arXiv:astro-ph/0702587.[178] S. Chang, G. D. Kribs, D. Tucker-Smith, and N. Weiner,Inelastic Dark Matter in Light of DAMA/LIBRA, Phys.Rev. D , 043513 (2009), arXiv:0807.2250 [hep-ph].[179] M. Y. Khlopov and C. Kouvaris, Composite dark matterfrom a model with composite Higgs boson, Phys. Rev.D , 065040 (2008), arXiv:0806.1191 [astro-ph].[180] B. Batell, M. Pospelov, and A. Ritz, Direct Detection ofMulti-component Secluded WIMPs, Phys. Rev. D ,115019 (2009), arXiv:0903.3396 [hep-ph].[181] P. W. Graham, R. Harnik, S. Rajendran, andP. Saraswat, Exothermic Dark Matter, Phys. Rev. D , 063512 (2010), arXiv:1004.0937 [hep-ph].[182] D. Spier Moreira Alves, S. R. Behbahani, P. Schuster,and J. G. Wacker, The Cosmology of Composite Inelas-tic Dark Matter, JHEP , 113, arXiv:1003.4729 [hep- ph].[183] M. McCullough and L. Randall, Exothermic Double-Disk Dark Matter, JCAP , 058, arXiv:1307.4095 [hep-ph].[184] G. Barello, S. Chang, and C. A. Newby, A Model Inde-pendent Approach to Inelastic Dark Matter Scattering,Phys. Rev. D , 094027 (2014), arXiv:1409.0536 [hep-ph].[185] M. Blennow, S. Clementz, and J. Herrero-Garcia, Self-interacting inelastic dark matter: A viable solutionto the small scale structure problems, JCAP , 048,arXiv:1612.06681 [hep-ph].[186] P. J. E. Peebles, Recombination of the primeval plasma,Astrophys. J. , 1 (1968).[187] Y. B. Zeldovich, V. Kurt, R. Sunyaev, et al. , Recom-bination of hydrogen in the hot model of the universe,Sov. Phys. JETP , 146 (1969).[188] W. Hu and N. Sugiyama, Toward understanding CMBanisotropies and their implications, Phys. Rev. D ,2599 (1995), arXiv:astro-ph/9411008.[189] M. Zaldarriaga and D. D. Harari, Analytic approach tothe polarization of the cosmic microwave background inflat and open universes, Phys. Rev. D , 3276 (1995),arXiv:astro-ph/9504085.[190] B. Hadzhiyska and D. N. Spergel, Measuring the Dura-tion of Last Scattering, Phys. Rev. D , 043537 (2019),arXiv:1808.04083 [astro-ph.CO].[191] F. Hoyle, On the fragmentation of gas clouds into galax-ies and stars., Astrophys. J. , 513 (1953).[192] M. J. Rees and J. P. Ostriker, Cooling, dynamics andfragmentation of massive gas clouds: clues to the massesand radii of galaxies and clusters., Mon. Not. Roy. As-tron. Soc. , 541 (1977).[193] M. R. C. McDowell, On the formation of H2 in H Iregions, The Observatory , 240 (1961).[194] P. J. E. Peebles and R. H. Dicke, Origin of the GlobularStar Clusters, Astrophys. J. , 891 (1968).[195] G. Shaw, G. J. Ferland, N. P. Abel, P. C. Stancil,and P. A. M. van Hoof, Molecular Hydrogen in Star-forming Regions: Implementation of its Microphysics inCLOUDY, Astrophys. J. , 794 (2005), arXiv:astro-ph/0501485 [astro-ph].[196] M. Tegmark, J. Silk, M. J. Rees, A. Blanchard, T. Abel,and F. Palla, How Small Were the First Cosmologi-cal Objects?, Astrophys. J. , 1 (1997), arXiv:astro-ph/9603007 [astro-ph].[197] V. Bromm, A. Ferrara, P. S. Coppi, and R. B. Lar-son, The fragmentation of pre-enriched primordial ob-jects, Mon. Not. Roy. Astron. Soc. , 969 (2001),arXiv:astro-ph/0104271 [astro-ph].[198] R. M. O’Leary and M. McQuinn, The Formation of theFirst Cosmic Structures and the Physics of the z ˜20Universe, Astrophys. J. , 4 (2012), arXiv:1204.1344[astro-ph.CO].[199] P. R. Shapiro and H. Kang, Hydrogen Molecules and theRadiative Cooling of Pregalactic Shocks, Astrophys. J. , 32 (1987).[200] S. P. Oh and Z. Haiman, Second-Generation Objects inthe Universe: Radiative Cooling and Collapse of Haloswith Virial Temperatures above 10 K, Astrophys. J. , 558 (2002), arXiv:astro-ph/0108071 [astro-ph].[201] J. L. Johnson and V. Bromm, The cooling of shock-compressed primordial gas, Mon. Not. Roy. Astron. Soc. , 247 (2006), arXiv:astro-ph/0505304 [astro-ph]. [202] G. D’Amico, P. Panci, A. Lupi, S. Bovino, andJ. Silk, Massive Black Holes from Dissipative DarkMatter, Mon. Not. Roy. Astron. Soc. , 328 (2018),arXiv:1707.03419 [astro-ph.CO].[203] M. Latif, A. Lupi, D. Schleicher, G. D’Amico, P. Panci,and S. Bovino, Black hole formation in the context ofdissipative dark matter, Mon. Not. Roy. Astron. Soc. , 3352 (2019), arXiv:1812.03104 [astro-ph.CO].[204] J. Pollack, D. N. Spergel, and P. J. Steinhardt,Supermassive Black Holes from Ultra-Strongly Self-Interacting Dark Matter, Astrophys. J. , 131 (2015),arXiv:1501.00017 [astro-ph.CO].[205] J. Choquette, J. M. Cline, and J. M. Cornell, Earlyformation of supermassive black holes via dark mat-ter self-interactions, JCAP , 036, arXiv:1812.05088[astro-ph.CO].[206] R. Mohapatra and V. L. Teplitz, Structures in the mir-ror universe, Astrophys. J. , 29 (1997), arXiv:astro-ph/9603049.[207] R. Foot, Have mirror stars been observed?, Phys. Lett.B , 83 (1999), arXiv:astro-ph/9902065.[208] R. N. Mohapatra and V. L. Teplitz, Mirror matterMACHOs, Phys. Lett. B , 302 (1999), arXiv:astro-ph/9902085.[209] R. Foot, A. Ignatiev, and R. Volkas, Physics of mirrorphotons, Phys. Lett. B , 355 (2001), arXiv:astro-ph/0011156.[210] R. N. Mohapatra and V. L. Teplitz, Mirror dark matterand galaxy core densities of galaxies, Phys. Rev. D ,063506 (2000), arXiv:astro-ph/0001362.[211] R. Mohapatra, S. Nussinov, and V. Teplitz, Mirror mat-ter as selfinteracting dark matter, Phys. Rev. D ,063002 (2002), arXiv:hep-ph/0111381.[212] R. Foot, H. Lew, and R. Volkas, Unbroken versus bro-ken mirror world: A Tale of two vacua, JHEP , 032,arXiv:hep-ph/0006027.[213] Z. Berezhiani, Mirror world and its cosmological con-sequences, Int. J. Mod. Phys. A , 3775 (2004),arXiv:hep-ph/0312335.[214] Z. Berezhiani, S. Cassisi, P. Ciarcelluti, and A. Pietrin-ferni, Evolutionary and structural properties of mir-ror star MACHOs, Astropart. Phys. , 495 (2006),arXiv:astro-ph/0507153.[215] D. Curtin and J. Setford, How To Discover Mirror Stars,Phys. Lett. B , 135391 (2020), arXiv:1909.04071[hep-ph].[216] D. Curtin and J. Setford, Signatures of Mirror Stars,JHEP , 041, arXiv:1909.04072 [hep-ph].[217] D. Curtin and J. Setford, Direct Detection ofAtomic Dark Matter in White Dwarfs, (2020),arXiv:2010.00601 [hep-ph].[218] J. Fan, A. Katz, L. Randall, and M. Reece, Double-Disk Dark Matter, Phys. Dark Univ. , 139 (2013),arXiv:1303.1521 [astro-ph.CO].[219] J. Fan, A. Katz, L. Randall, and M. Reece, Dark-Disk Universe, Phys. Rev. Lett. , 211302 (2013),arXiv:1303.3271 [hep-ph].[220] M. R. Buckley and A. DiFranzo, Collapsed Dark Mat-ter Structures, Phys. Rev. Lett. , 051102 (2018),arXiv:1707.03829 [hep-ph].[221] S. Tulin and H.-B. Yu, Dark Matter Self-interactionsand Small Scale Structure, Phys. Rept. , 1 (2018),arXiv:1705.02358 [hep-ph].[222] D. Tseliakhovich and C. Hirata, Relative velocity of dark matter and baryonic fluids and the formation ofthe first structures, Phys. Rev. D , 083520 (2010).[223] D. Tseliakhovich, R. Barkana, and C. M. Hi-rata, Suppression and spatial variation ofearly galaxies and minihaloes, Monthly Noticesof the Royal Astronomical Society , 906(2011), https://academic.oup.com/mnras/article-pdf/418/2/906/3692552/mnras0418-0906.pdf.[224] T. H. Greif, S. D. M. White, R. S. Klessen, andV. Springel, The Delay of Population III Star Formationby Supersonic Streaming Velocities, The AstrophysicalJournal , 147 (2011).[225] S. Naoz, N. Yoshida, and N. Y. Gnedin, Simulations ofEarly Baryonic Structure Formation with Stream Ve-locity. I. Halo Abundance, The Astrophysical Journal , 128 (2012).[226] S. Naoz, N. Yoshida, and N. Y. Gnedin, Simulations ofEarly Baryonic Structure Formation with Stream Ve-locity. II. The Gas Fraction, The Astrophysical Journal , 27 (2012).[227] A. T. P. Schauer, S. C. O. Glover, R. S. Klessen,and D. Ceverino, The influence of streaming veloc-ities on the formation of the first stars, MonthlyNotices of the Royal Astronomical Society ,3510 (2019), https://academic.oup.com/mnras/article-pdf/484/3/3510/27714961/stz013.pdf.[228] A. T. Schauer, S. C. Glover, R. S. Klessen, andP. Clark, The influence of streaming velocities andlyman-werner radiation on the formation of the firststars, arXiv:2008.05663 (2020).[229] B. Greig and A. Mesinger, The global history of reion-ization, Mon. Not. Roy. Astron. Soc. , 4838 (2017),arXiv:1605.05374 [astro-ph.CO].[230] R. Bouwens, G. Illingworth, P. Oesch, J. Caruana,B. Holwerda, R. Smit, and S. Wilkins, Reionization af-ter Planck: The Derived Growth of the Cosmic Ioniz-ing Emissivity now matches the Growth of the GalaxyUV Luminosity Density, Astrophys. J. , 140 (2015),arXiv:1503.08228 [astro-ph.CO].[231] S. Mitra, T. R. Choudhury, and A. Ferrara, Cosmicreionization after Planck, Mon. Not. Roy. Astron. Soc. , L76 (2015), arXiv:1505.05507 [astro-ph.CO].[232] A. Gorce, M. Douspis, N. Aghanim, and M. Langer,Observational constraints on key-parameters of cos-mic reionisation history, Astron. Astrophys. , A113(2018), arXiv:1710.04152 [astro-ph.CO].[233] J. Park, A. Mesinger, B. Greig, and N. Gillet, Infer-ring the astrophysics of reionization and cosmic dawnfrom galaxy luminosity functions and the 21-cm sig-nal, Mon. Not. Roy. Astron. Soc. , 933 (2019),arXiv:1809.08995 [astro-ph.GA].[234] M. Fukugita, C. Hogan, and P. Peebles, The Cos-mic baryon budget, Astrophys. J. , 518 (1998),arXiv:astro-ph/9712020.[235] M. Fukugita and P. E. Peebles, The Cosmic energyinventory, Astrophys. J. , 643 (2004), arXiv:astro-ph/0406095.[236] J. M. Shull, B. D. Smith, and C. W. Danforth, TheBaryon Census in a Multiphase Intergalactic Medium:30% of the Baryons May Still be Missing, Astrophys. J. , 23 (2012), arXiv:1112.2706 [astro-ph.CO].[237] F. Nicastro et al. , Observations of the missing baryonsin the warm-hot intergalactic medium, Nature , 406(2018), arXiv:1806.08395 [astro-ph.GA].[238] de Graaff, Anna, Cai, Yan-Chuan, Heymans, Catherine,and Peacock, John A., Probing the missing baryons withthe sunyaev-zel´dovich effect from filaments, A&A ,A48 (2019).[239] S. D. Johnson et al. , The physical origins of the identi-fied and still missing components of the warm–hot in-tergalactic medium: Insights from deep surveys in thefield of blazar 1es1553+113, The Astrophysical Journal , L31 (2019).[240] O. E. Kov´acs, ´A. Bogd´an, R. K. Smith, R. P. Kraft, andW. R. Forman, Detection of the missing baryons towardthe sightline of h1821+643, The Astrophysical Journal , 83 (2019).[241] J.-P. Macquart et al. , A census of baryons in the Uni-verse from localized fast radio bursts, Nature581