A fake Interacting Dark Energy detection?
MMNRAS , 1–5 (2020) Preprint 20 October 2020 Compiled using MNRAS L A TEX style file v3.0
A fake Interacting Dark Energy detection?
Eleonora Di Valentino ★ and Olga Mena Jodrell Bank Center for Astrophysics, School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester, M13 9PL, UK IFIC, Universidad de Valencia-CSIC, 46071, Valencia, Spain
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
Models involving an interaction between the Dark Matter and the Dark Energy sectors have been proposed to alleviate thelong standing Hubble constant tension. In this paper we analyze whether the constraints and potential hints obtained for theseinteracting models remain unchanged when using simulated Planck data. Interestingly, our simulations indicate that a dangerousfake detection for a non-zero interaction among the Dark Matter and the Dark Energy fluids could arise when dealing withcurrent CMB Planck measurements alone. The very same hypothesis is tested against future CMB observations, finding thatonly cosmic variance limited polarization experiments, such as PICO or PRISM, could be able to break the existing parameterdegeneracies and provide reliable cosmological constraints. This paper underlines the extreme importance of confronting theresults arising from data analyses with those obtained with simulations when extracting cosmological limits within exoticcosmological scenarios.
Key words: cosmic background radiation – cosmological parameters – dark energy
Despite the wonderful agreement of present cosmological measure-ments with the canonical Λ CDM model, some tensions betweendifferent observations have started to question the validity of thestandard cosmological model. In particular, a significant role is theone played by the long standing Hubble constant tension at 4 . 𝜎 between the estimate from 2018 Planck released data Aghanim et al.(2020) and the value measured by R19, i.e. the SH0ES collabora-tion Riess et al. (2019) (see Di Valentino et al. (2020a) for a recentoverview). These two recent measurements are supported by otherearly and late time cosmological probes, respectively, making moredifficult the possibility of isolating systematic effects in the experi-ments that could bias the data in the same direction. For this reason,a gigantic effort has been made by the community to build modelsbeyond the standard Λ CDM that could explain and alleviate the 𝐻 disagreement with a modification of the cosmological scenario.Plenty of work has been devoted to early modifications of theexpansion history, such adding either an Early Dark Energy com-ponent Pettorino et al. (2013); Poulin et al. (2019); Karwal &Kamionkowski (2016); Sakstein & Trodden (2020); Niedermann& Sloth (2019); Akarsu et al. (2020); Ye & Piao (2020); Agrawalet al. (2019a); Lin et al. (2019); Berghaus & Karwal (2020); Smithet al. (2020); Lucca (2020) or extra relativistic species at recombina-tion Anchordoqui & Goldberg (2012); Jacques et al. (2013); Wein-berg (2013); Anchordoqui et al. (2013); Carneiro et al. (2019); Paulet al. (2019); Di Valentino et al. (2016a); Green et al. (2019); Ferreira& Notari (2018); Gelmini et al. (2019); Di Valentino et al. (2016b);Poulin et al. (2018); Baumann et al. (2016); Barenboim et al. (2017);Zeng et al. (2019); Allahverdi et al. (2014). Interestingly, these solu- ★ E-mail: [email protected] tions are promising for both solving the 𝐻 tension and lowering thesound horizon at the drag epoch Knox & Millea (2020); Evslin et al.(2018), despite the fact that they do not provide a value for the Hubbleconstant large enough to be in agreement with R19 Arendse et al.(2020). On the other hand, late time modifications of the expansionhistory, such as the phantom Dark Energy Aghanim et al. (2020);Yang et al. (2019c,a); Di Valentino et al. (2020c); Vagnozzi (2020);Di Valentino et al. (2020b); Keeley et al. (2019); Joudaki et al. (2017)or the Phenomenologically Emergent Dark Energy Li & Shafieloo(2019); Pan et al. (2020); Rezaei et al. (2020); Liu & Miao (2020);Li & Shafieloo (2020); Yang et al. (2020c) scenarios, perform betterin the 𝐻 resolution but leave the sound horizon unaltered.Within this context, a large number of the models proposed in-volves the encouraging possibility of an interaction between DarkMatter and Dark Energy (IDE models Pettorino (2013); Salvatelliet al. (2014); Kumar & Nunes (2016); Di Valentino et al. (2017);Kumar & Nunes (2017); Van De Bruck & Mifsud (2018); Solàet al. (2017); Yang et al. (2018b,a, 2019d); Martinelli et al. (2019);Di Valentino et al. (2020d,e); Benevento et al. (2020); Gómez-Valentet al. (2020); Lucca & Hooper (2020); Yang et al. (2020b,a, 2019b);Agrawal et al. (2019b); Anchordoqui et al. (2020b); Johnson &Shankaranarayanan (2020); Anchordoqui et al. (2020a)). This solu-tion naturally releases the Hubble constant tension, because it playswith the geometrical degeneracy existing between the parameter gov-erning the interacting rate and the dark matter mass energy density,which is modified by the flux of energy exchanged between the darkmatter and the dark energy fluids.In this paper we scrutinize if the current constraints obtained forthese IDE models are reliable simulating the Planck data, and iffuture CMB experiments can improve the soundness of present IDEbounds. We present in Sec. 2 the approach used in this paper to © a r X i v : . [ a s t r o - ph . C O ] O c t Eleonora Di Valentino and Olga Mena
Table 1.
Experimental specifications.Configuration Channel Beam Δ 𝑃 ℓ 𝑚𝑎𝑥 ℓ 𝑚𝑖𝑛 𝑓 sky GHz arcmin 𝜇𝐾 -arcminPICO 75 10 . . . . . . . . . . . . . . . .
35 6 .
08 6000 2 0 . .
12 5 . .
27 4 . .
80 3 . .
16 2 . .
96 2 . .
48 1 . .
72 4 . .
44 4 . .
28 3 . .
04 4 . .
00 4 . simulate and analyse the mock datasets. Section 3 contains our mainresults. We conclude in Sec. 4. For simulating current and future CMB measurements, we shallfollow the approach used in several white papers and commonlyexploited in the literature, see e.g. Refs. Di Valentino et al.(2018a); Hanany et al. (2019); Delabrouille et al. (2019); Cappar-elli et al. (2018); Di Valentino et al. (2018b); Renzi et al. (2018a,b);Di Valentino et al. (2019). The fiducial cosmology is a vanilla flat Λ CDM model compatible with Planck TT,TE,EE + lowE measure-ments, and therefore with a null coupling between Dark Matter andDark Energy. The values of the parameters assumed for our simulateddata are reported in the second column of the Tables 2 and 3.We compute the theoretical CMB angular power spectra 𝐶 𝑇 𝑇ℓ , 𝐶 𝑇 𝐸ℓ , 𝐶 𝐸𝐸ℓ , 𝐶 𝐵𝐵ℓ for temperature, cross temperature-polarizationand 𝐸 and 𝐵 modes polarization using the publicly available Boltz-mann code camb Lewis et al. (2000). The assumed instrumental noisereads as 𝑁 ℓ = 𝑤 − exp ( ℓ ( ℓ + ) 𝜃 / ) , (1)where 𝑤 − is experimental sensitivity expressed in ( 𝜇𝐾 -rad ) and 𝜃 is the experimental FWHM angular resolution of the beam. Thetotal variance of the multipoles 𝑎 ℓ𝑚 will be given by the sum of thefiducial 𝐶 ℓ ’s plus the instrumental noise 𝑁 ℓ . The simulated Planckdata also has a contribution from experimental noise similar to thatpresented in the 2018 Planck legacy release analyses Akrami et al.(2020).Concerning future CMB observations, we shall consider two fu-ture CMB experiments, PICO Hanany et al. (2019) and PRISM De-labrouille et al. (2019), and we shall generate the noise spectra withthe noise properties shown in Tab. 1. We also simulate BAO data,computing the mean values of the BAO observables using the Λ CDMfiducial cosmology assumed in this analysis, and taking the uncer-tainties and covariance matrices of the original BAO data listed in Sec. 5.1 of the Planck parameters paper Aghanim et al. (2020), tobuild the likelihood.We perform Monte Carlo Markov chain (MCMC) analyses to cur-rent and future mock data (which are generated assuming the minimal Λ CDM scenario) assuming a non-zero coupling 𝜉 between the darkmatter and the dark energy fluids. In particular, we consider a class ofmodels where the Dark Matter and Dark Energy continuity equationsare coupled as follows: (cid:164) 𝜌 𝑐 + H 𝜌 𝑐 = 𝑄 , (2) (cid:164) 𝜌 𝑥 + H ( + 𝑤 ) 𝜌 𝑥 = − 𝑄 , (3)where the dot corresponds to the derivative with respect to confor-mal time 𝜏 , H is the conformal expansion rate of the universe, 𝜌 𝑐 and 𝜌 𝑥 are the dark matter and dark energy mass energy densitiesrespectively, the dark energy equation of state 𝑤 is assumed to beconstant, and the coupling function 𝑄 governing the interaction ratebetween the two dark components is given by: 𝑄 = 𝜉 H 𝜌 𝑥 , (4)In order to derive the cosmological constraints, we shall compare thetheoretical spectra with the mock datasets, considering a Gaussianlikelihood L given by − L = ∑︁ ℓ ( ℓ + ) 𝑓 sky (cid:18) 𝐷 | ¯ 𝐶 | + ln | ¯ 𝐶 || ˆ 𝐶 | − (cid:19) , (5)where ¯ 𝐶 and ˆ 𝐶 are the assumed fiducial and theoretical plus noisepower spectra, 𝐷 is: 𝐷 = ˆ 𝐶 𝑇 𝑇ℓ ¯ 𝐶 𝐸𝐸ℓ ¯ 𝐶 𝐵𝐵ℓ + ¯ 𝐶 𝑇 𝑇ℓ ˆ 𝐶 𝐸𝐸ℓ ¯ 𝐶 𝐵𝐵ℓ + ¯ 𝐶 𝑇 𝑇ℓ ¯ 𝐶 𝐸𝐸ℓ ˆ 𝐶 𝐵𝐵ℓ − ¯ 𝐶 𝑇 𝐸ℓ (cid:16) ¯ 𝐶 𝑇 𝐸ℓ ˆ 𝐶 𝐵𝐵ℓ + 𝐶 𝑇 𝐸ℓ ¯ 𝐶 𝐵𝐵ℓ (cid:17) . (6)and 𝑓 𝑠𝑘𝑦 is the sky fraction measured by the experiment (seeRefs. Capparelli et al. (2018); Di Valentino et al. (2018a); Hananyet al. (2019); Delabrouille et al. (2019) for more details).For our numerical analysis, we make use of both the originalversion and a modified version with the IDE scenario of the pub-licly available MCMC code CosmoMC
Lewis & Bridle (2002) pack-age (see http://cosmologist.info/cosmomc/ ), implementingan efficient sampling of the posterior distribution using the fast/slowparameter decorrelations Lewis (2013), and with a convergence diag-nostic based on the Gelman-Rubin statistics Gelman & Rubin (1992).
Table 2 presents the constraints at 68% CL on the seven varyingcosmological parameters of the IDE model with a dark energy equa-tion of state 𝑤 = − . 𝑤 = − .
999 to the Λ CDM case (i.e. 𝑤 = − 𝜉 among the dark sectors.Therefore, the results depicted in Tab. 3 allow us to quantify the errorintroduced when considering 𝑤 slightly different from −
1, i.e. thevalue assumed in the fiducial cosmology, and serve us as a direct testof the reliability of our method. Notice that we can recover with anexquisite precision the fiducial values of the cosmological parame-ters chosen to create the mock datasets with all the current and future
MNRAS , 1–5 (2020) fake Interacting Dark Energy detection? cosmological observations considered in this work. These results en-sure the robustness of our approach and warrant the strength of thederived conclusions, excluding the presence of spurious biases.Correlations between the cosmological parameters play a crucialrole when exploring exotic scenarios. Indeed, it is well known thatthe geometric degeneracy present for the IDE models in the CMBdamping tail between the matter mass-energy density and the Hub-ble constant it is a straightforward solution to ease the 𝐻 tension.CMB observations constrain the quantity Ω 𝑚 ℎ using the positionof the acoustic peaks, and therefore a larger value of 𝐻 can be easilyobtained by means of a lower value of Ω 𝑚 , which is precisely whathappens within the IDE models considered here (see Eq. (4)) whenthe coupling satisfies the condition 𝜉 <
0, due to the fact that theenergy flows from the dark matter sector to the dark energy one.Therefore, parameter degeneracies may potentially lead to fake in-dications for exotic physics. If we assume that nature has chosenthe minimal Λ CDM scenario, but the observational data analysis isperformed assuming an IDE Model, i.e. we consider the coupling 𝜉 free to vary when we analyse the mock datasets, we find that aPlanck-like experiment (i.e. cosmic variance limited in temperaturebut not in polarization) is not powerful enough to recover the fidu-cial cosmological model in this case. Note from the results shown inTab. 2, that due to the strong correlation present between the standardand the exotic physics parameters, an evidence at more than 3 𝜎 for acoupling between dark matter and dark energy different from zero isfound, i.e. − . < 𝜉 < − .
02 at 99% CL. This strong significancefor the presence of a coupling leads to a corresponding reduction inthe current cold dark matter mass energy density estimate and anincrease of 𝜃 , the angular size of the horizon at decoupling. There-fore, the fake detection, at more than 99% CL, for a dark matter-darkenergy exchange rate, see the black curve in Fig. 1, is completely dueto the cosmological parameter degeneracies. This outcome stronglyunderlines the importance of confronting the results arising from thedata analyses with those obtained with simulations. The inclusion ofBAO data, a mock dataset built using the same fiducial cosmologi-cal model than that of the CMB, helps in breaking the degeneracy,providing a lower limit for the coupling 𝜉 in perfect agreement withzero, see the fourth column of Tab. 2 and the red curve in Fig. 1.Future observations from PICO or PRISM, cosmic variance-limited polarization CMB experiments, will be able to break thecorrelations between the parameters without the addition of any ex-ternal datasets. These future observations will be able to recover(alone) the true, nature fiducial cosmology within one standard de-viation, see Tab. 2 and the green and blue curves in Fig. 1. Side by side to the early expansion history modifications, that are notefficient in resolving completely the 𝐻 tension, and the late-timesolutions, that solving the Hubble constant problem, can not recon-cile instead the BAO data, there are the interacting Dark Matter-DarkEnergy models. We have studied in this paper whether the constraintsobtained for these interacting models derived from current observa-tions, see for example Di Valentino et al. (2020e,d), are fully sup-ported by simulated Planck data. Intriguingly, we have found here thatdue to the correlation between the parameters, there exists a danger-ous fake detection for a non-zero Dark Matter-Dark Energy couplingat many standard deviations when dealing with CMB observations − − − − − ξ P / P m a x PlanckPlanck+BAOPICOPRISM
Figure 1.
One-dimensional marginalized posterior distributions for the pa-rameter 𝜉 governing the dark matter-dark energy interactions, from differentdata combinations arising from our MCMC analyses, as reported in Table 2,see text for details. from the Planck satellite. As a second step, we have tested thesame hypothesis exploiting simulations for future cosmic variance-limited polarization CMB experiments, such as PICO or PRISM.We have found that these experiments could be able to break theexisting parameter correlations, providing reliable constraints on thecosmological parameters. While these results are obtained for a giveninteracting model with an energy exchange rate proportional to thedark energy energy density and other models could not lead to thevery same fake detection effect, the main end of our study is toemphasize the utmost importance of confronting the results arisingfrom data analyses to those obtained with simulations before deriv-ing any final conclusions concerning the scrutinized cosmologicalmodel, rather than focus on a particular scenario. ACKNOWLEDGEMENTS
We thank Alessandro Melchiorri and Sunny Vagnozzi for the en-lightening discussions. EDV was supported from the European Re-search Council in the form of a Consolidator Grant with number681431. O.M. is supported by the Spanish grants FPA2017-85985-P,PROMETEO/2019/083 and by the European ITN project HIDDeN(H2020-MSCA-ITN-2019//860881-HIDDeN). It is worthwhile to note here that, using exactly the same Planck simulateddata in Di Valentino et al. (2019), it is shown in Fig.1 that a Planck-likeexperiment is able to constrain Ω 𝑘 = A similar simulated study applied to interacting models with the energyexchange rate ∝ 𝜌 𝑐 will be carried out elsewhere. MNRAS000
We thank Alessandro Melchiorri and Sunny Vagnozzi for the en-lightening discussions. EDV was supported from the European Re-search Council in the form of a Consolidator Grant with number681431. O.M. is supported by the Spanish grants FPA2017-85985-P,PROMETEO/2019/083 and by the European ITN project HIDDeN(H2020-MSCA-ITN-2019//860881-HIDDeN). It is worthwhile to note here that, using exactly the same Planck simulateddata in Di Valentino et al. (2019), it is shown in Fig.1 that a Planck-likeexperiment is able to constrain Ω 𝑘 = A similar simulated study applied to interacting models with the energyexchange rate ∝ 𝜌 𝑐 will be carried out elsewhere. MNRAS000 , 1–5 (2020) Eleonora Di Valentino and Olga Mena
Table 2.
68% CL bounds on the cosmological parameters assuming that nature has chosen the minimal Λ CDM scenario but the observational data analysis isperformed assuming an IDE Model with a dark energy equation of state 𝑤 = − . Parameters Fiducial model Planck Planck+BAO PICO PRISM Ω 𝑏 ℎ . . ± . . ± . . ± . . ± . Ω 𝑐 ℎ . . + . − . . + . − . . + . − . . + . − . 𝜃 𝑀𝐶 . . + . − . . + . − . . + . − . . + . − . 𝜏 . . + . − . . ± . . + . − . . + . − . 𝑛 𝑠 . . ± . . ± . . ± . . ± . ( 𝐴 𝑠 ) .
045 3 . + . − . . ± .
019 3 . + . − . . ± . 𝜉 − . + . − . > − . > − . > − . Table 3.
68% CL bounds on the cosmological parameters assuming that nature has chosen the minimal Λ CDM scenario (with 𝑤 = −
1) but the observational data analysis is perfomed with a dark energy equation of state 𝑤 = − . Parameters Fiducial model Planck Planck+BAO PICO PRISM Ω 𝑏 ℎ . . ± . . ± . . ± . . ± . Ω 𝑐 ℎ . . ± . . ± . . ± . . ± . 𝜃 𝑀𝐶 . . ± . . ± . . ± . . ± . 𝜏 . . ± .
010 0 . ± . . ± . . ± . 𝑛 𝑠 . . ± . . ± . . ± . . ± . ( 𝐴 𝑠 ) .
045 3 . ± .
019 3 . ± .
019 3 . ± . . ± . DATA AVAILABILITY
The simulated data underlying this article will be shared on reason-able request to the corresponding author.
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