Quantum creation of a universe-antiuniverse pair
QQuantum creation of a universe-antiuniverse pair
S. J. Robles-P´erez
1, 2 Canadian Quantum Research Center, 204-3002 32 Ave Vernon, BC V1T 2L7, Canada Estaci´on Ecol´ogica de Biocosmolog´ıa, Pedro de Alvarado, 14, 06411 Medell´ın, Spain (Dated: February 25, 2020)If one analyses the quantum creation of the universe, it turns out that the most natural way inwhich the universes can be created is in pairs of universes whose time flow is reversely related. Itmeans that the matter that propagates in one of the universes can be seen, from the point of view ofthe other universe, as antimatter, and viceversa. They thus form a universe-antiuniverse pair. Froma global point of view, i.e. from the point of view of the whole multiverse ensemble, the creation ofuniverses in universe-antiuniverse pairs restores the matter-antimatter asymmetry observed in eachindividual universe and it might provide us with distinguishable imprints of the whole multiverseproposal.
PACS numbers: 98.80.Qc, 03.65.w
I. INTRODUCTION
It has been known for a long time in quantum cosmol-ogy that the creation of the universe can be given in pairs.For instance, the Hartle-Hawking no boundary condition[1] gives rise a quantum state that can be written in thesemiclassical regime as φ = φ + + φ − ≈ e + i (cid:126) S ( a,ϕ ) + e − i (cid:126) S ( a,ϕ ) , (1)where S ( a, ϕ ) is the Einstein-Hilbert action of a DeSitterlike spacetime that is formed from the corresponding Eu-clidean DeSitter instanton [2]. Typically, the componentsof the superposition state (1) have been interpreted asrepresenting the contracting and the expanding branchesof the DeSitter spacetime. Which component representsthe contracting branch and which one represents the ex-panding one is a matter of convention because, as it ispointed out in Ref. [3], there is no absolute notion oftime in the universe so one can reverse the direction ofthe time variable and then, φ + and φ − would interchangetheir role. However, if one investigates further the ap-pearance of the time variable in the two universes onerealises [4] that the physical time variables of the the twouniverses represented in (1) must be reversely related.Then, according to the CP T theorem, the matter con-tent in the two branches must be CP related, where C and P are the charge conjugation and the parity reversaloperations, respectively. On the other hand, it is alsoshown in Ref. [3] that from the point of view of thethermodynamical arrow of time both branches in (1) de-scribe an expanding universe. These two reasons makethat the superposition state (1) can more naturally beinterpreted as two expanding universes, one of which isfilled with matter and the other is filled with antimatter,having these two terms always a relative meaning withrespect to each other. The quantum state (1) can then beinterpreted as representing the quantum superposition ofa universe-antiuniverse pair [4].The creation of the universe in a universe-antiuniversepair would thus restore the matter-antimatter asymme-try observed from the point of view of the single universe. The idea of a time reversal relation between a pair of uni-verses to explain the matter-antimatter asymmetry ob-served in our universe is not new, actually. It dates backat least to the early 70’s [5] and it was even posed bySakharov in the early 80’s too [6]. However, for somereason these models have not received the attention theydeserve. One of these reasons may be that the consid-eration of other universes has typically been consideredan unphysical or a metaphysical proposal in the sense ofbeing unobservable and therefore untestable. The ideabehind the rejection can be sketched as follows: on theone hand, if some event is observable, then, there is atime-like or null path joining together the original eventand the observation event and, thus, these two eventsbelong to the same universe; and, on the other hand,if a given event belongs to a different universe, whichfrom the classical point of view is disconnected to theobserver’s universe, then, any two events of the two uni-verses cannot be joined by a time like or null path sothe original event cannot be observed. Thus, the mul-tiverse has typically been considered as a non falsifiableproposal.However, at least three caveats must be raised at thispoint. First, a theoretical consistency of the theory isan important sign to at least taking the proposal intoconsideration. After all we can infer the existence of anotherwise unobservable stellar object (say a black hole)from the theoretical consistency of the perturbed motionof the observable companion, and symmetry consisten-cies made theoretical physicists to predict the existence ofthe charm quark; not to talk about the unobserved ’darkmatter’ that is basically supported by consistency argu-ments. Second, observability and falsifiability are not thesame thing, as it is clearly argued in Ref. [7] (see also, Tegmark poses the following example: a theory stating that thereare 666 parallel universes, all of which are devoid of oxygen,makes the testable prediction that we should observe no oxygenhere, and is therefore ruled out by observation , cfr. Ref. [7], p.105. a r X i v : . [ g r- q c ] F e b Ref. [8] for a recent review). Third, the classical argu-ment exposed above rejecting the multiverse is the typicalclassical way of thinking that has constantly been chal-lenged by the quantum theory from the very beginning(let us note, for instance, the well-known EPR paradox[9]). More concretely, the direct non-observability, in theclassical sense, does not exclude the possibility of mea-suring observable effects derived from the existence ofquantum correlations or entanglement between the stateof some matter field in two distant places. For instance,in Ref. [10] it is shown with the help of the parametricamplifier setup of quantum optics that an isolated ob-server can infer the existence of an unobservable partnermode of the radiation field only from the photon num-ber distribution of the light beam that the observer de-tects. Similarly, one can show [11] that the existence ofa partner antiuniverse would leave not only observablebut also distinguishable imprints in the properties of auniverse like ours, making falsifiable the creation of uni-verses in universe-antiuniverse pairs as well as the wholemultiverse proposal.This paper is outlined as follows. In Sect. II we shallreview the paradigmatic example of the creation of a De-Sitter spacetime. We shall obtain the quantum state (1)and interpret it as the superposition state that representsan expanding and a contracting universes, as usual. InSect. III we shall analyse the matter content of the uni-verses and the appearance of the physical time variable,i.e. the one that appears in the Schr¨odinger equation.We shall show that the physical time variables of the twouniverses must be reversely related and that, in termsof the time variable measured by the inhabitants of theuniverse, both universes are expanding universes with theobserver’s universe initially filled of matter and the part-ner universe initially filled with antimatter. In Sect. IVwe shall review the kind of observable imprints that thecreation of the universe in a universe-antiuniverse pairshould leave, and finally, in Sect. V we shall briefly drawsome conclusions.
II. QUANTUM CREATION OF THE UNIVERSE
The dynamics of the gravitational field can be obtainedin the Lagrangian framework from the variational princi-ple of the Einstein-Hilbert action, which in the canonicalform is essentially the integral over the spacetime mani-fold M of the Ricci scalar plus some boundary term (forthe details see, for instance, Ref. [12]). The essence ofEinstein’s geometrodynamics is the foliation of the space-time by a set of spatial sections distributed along the timevariable. In that case, the evolution of the universe canbe seen as the time evolution of the metric tensor h ij ( t )of the 3-dimensional spatial hypersurface Σ t . To this As Wheeler says [13],
Eintein’s geometrodynamics deals with thedynamics of -geometry, not -geometry! (emphasis his). action one must add the action of the matter fields thatpropagate in the background spacetime. They togetherform the total action from which one can obtain the fieldequations of the whole universe. In general, they are verycomplicated if not impossible to solve. However, in cos-mology we are mainly interested in describing a universethat is created with some degree of symmetry. We knowthat the fluctuations of the gravitational field are lengthdependent and they become of order of the metric tensorat the Planck length [14]. Therefore, if we assume thatthe universe is created with a length scale well above fromthe Planck length, then, it can be described, at least asa first approximation, by a homogeneous and isotropicmetric with small inhomogeneities propagating therein.Therefore, let us consider the FRW metric ds = − N dt + a ( t ) d Ω , (2)where a ( t ) is the scale factor and d Ω is the line elementon the 3-sphere of unit radius ; and a scalar field repre-senting the matter content of the universe given by, ϕ ( t, (cid:126)x ) = ϕ ( t ) + (cid:88) n f n ( t ) Q n ( (cid:126)x ) , (3)where ϕ ( t ) is the homogeneous mode, Q n ( (cid:126)x ) is the scalarharmonic on the 3-sphere, and f n ( t ) represent the inho-mogeneities of the matter field. The homogeneous modecontains the major part of the energy of the matter fieldand contributes to the evolution of the background space-time, and the inhomogeneities can be seen, at least forthe modes with a large value of n ≡ | n | , as the particlesof the field that propagate in an evolving backgroundspacetime. If the inhomogeneities are sufficiently smallthe total action decouples and can be written as [11, 15] S = 12 (cid:90) dtN (cid:18) − a ˙ a N + a − H a (cid:19) (4)+ 12 (cid:90) dtN a (cid:88) n ˙ f n N − ω n f n , (5)where ω n = n − a + m , (6)with m the mass of the scalar field. The first term in(4) is the action of the background spacetime. The timederivative of the homogeneous mode of the scalar fielddoes not appear because we have assumed the typicalconditions for the initial inflationary stage of the uni-verse, ˙ ϕ (cid:28)
1, and, 2 V ( ϕ ) ≡ H (cid:29)
1, in Planck units.The second term in (4) is the action of a set of uncoupledharmonic oscillators with time dependent ’mass’, givenby M = a ( t ), and time dependent frequency given by We are assuming closed spatial sections of the spacetime. (6). The lapse function must be retained in (4) until thevariation of the action with respect to N is performed,and then will be set to one.Let us first consider the dynamics of the backgroundspacetime by neglecting the inhomogeneities. In thatcase, the invariance of the action with respect to the lapsefunction gives rise the classical Hamiltonian constraint, H = 12 a (cid:0) − p a + H a − a (cid:1) = 0 , (7)which in terms of the time derivative of the scale factor, p a = − a ˙ a , can be written as˙ a = (cid:112) H a − . (8)It has the well-known solution, a ( t ) = a cosh Ht , thatrepresents a universe that contracts from an infinite vol-ume until it reaches the minimum volume element, givenby a , and then starts expanding again. For this reason,the two branches of the solution (8) are called the con-tracting and the expanding branches of the universe (see,Fig. 1).Quantum mechanically, the quantum state of the uni-verse is represented by the wave function that is the solu-tion of the Wheeler-DeWitt equation obtained from thecanonical quantisation of the classical momentum in (7), p a → − i (cid:126) ∂∂a , i.e. (cid:126) ∂ φ ( a ) ∂a + Ω ( a ) φ ( a ) = 0 , (9)where Ω ( a ) = H a − a . (10)We do not know the exact solutions of (9) but far fromthe turning point, a = H − , we can use the WKB wavefunctions. Moreover, the turning point splits the min-isuperspace in two parts with two different regimes forthe wave function φ ( a ). For the value a > a , the wavefunction is in the oscillatory regime with WKB solutionsgiven by the complex exponentials, φ ± ∝ e ± i (cid:126) S ( a ) , where S ( a ) = (cid:82) Ω( a (cid:48) ) da (cid:48) . On the other hand, the value, a < a ,defines the tunnelling region of the minisuperspace wherethe wave function is given by a linear combination ofthe real exponentials , e ± (cid:126) I ( a ) , with I ( a ) = (cid:82) | Ω( a (cid:48) ) | da (cid:48) .The exact combination of wave functions depends on theboundary condition imposed on the state of the universe.For instance, with the Hartle-Hawking no boundary pro-posal [1], the quantum state of the universe in the oscil-latory region turns out to be φ ( a ) = φ + + φ − ≈ √ Ω e + i (cid:126) S ( a ) + 1 √ Ω e − i (cid:126) S ( a ) . (11) The universe is said then to be created ’from nothing’ meaningby that that it is created from a quantum tunnelling process intothe classically allowed region of the minisuperspace.
The customary interpretation of the wave function (11)is that it represents two universes, which according to therelation − a ˙ a = p a ≈ (cid:104) φ ± | ˆ p a | φ ± (cid:105) ∼ ± ∂S∂a ⇒ ˙ a = ∓ a ∂S∂a , (12)one, φ − , is expanding and the other, φ + , is contracting.A decoherence process makes that the two universes canrapidly be considered independently [16, 17]. The typi-cal choice is then to consider the expanding branch as therepresentative of our universe and disregard the contract-ing one as not being physically significant. However, weshall see in the next sections that the two branches mayform a non-separable state with important consequences. III. MATTER-ANTIMATTER CONTENT OFTHE UNIVERSE
Let us now analyse the matter content of the universeby considering the total Hamiltonian constraint, (cid:16) ˆ H + ˆ H m (cid:17) φ ( a, f n ) = 0 , (13)where ˆ H m is the Hamiltonian of the inhomogeneities ofthe matter field. The solution of (13) is not much differ-ent to the wave function (11). It contains now a factorthat gathers all the dependence on the inhomogeneousdegrees of freedom, φ ± ( a, f n ) = 1 (cid:112) Ω( a ) e ± i (cid:126) S ( a ) ψ ± ( a, f n ) . (14)It comes now one of the most beautiful features of quan-tum cosmology, the appearance of the classical time vari-able and the quantum dynamics of the matter fields.If one inserts the wave function (14) into the Wheeler-DeWitt equation (13), assumes that the backgroundspacetime is varying very slow compared with the varia-tion of the matter fields, and solves it order by order in (cid:126) , one obtains at order (cid:126) the Hamilton-Jacobi equation − (cid:18) ∂S∂a (cid:19) + Ω = 0 , (15)which is equivalent to the classical momentum constraint(7) if one identifies the momentum conjugated to thescale factor p a with ± ∂S∂a . In that case, Eq. (15) showsthat the solutions for the classical momentum of thebackground spacetime are, p a = ± Ω. These values ofthe momentum p a are associated to the two branches in(11) so the creation of universes in pairs would thus con-serve the total amount of momentum conjugated to thescale factor. Furthermore, we can define a time variable, t ± , called the WKB time [15], as ∂∂t ± = ∓ a ∂S∂a ∂∂a , (16)in terms of which one recovers the classical Friedmannequation (8), ˙ a = ∓ a ∂S∂a = ∓ (cid:112) H a − . (17)On the other hand, at order (cid:126) in H one obtains ∓ i (cid:126) a ∂S∂a ∂∂a ψ ± = ˆ H m ψ ± , (18)which is essentially a Schr¨odinger like equation if onerealises that the l.h.s. is basically the derivative of thewave function ψ ± with respect to the time variable of theclassical background defined in (16). However, there is afreedom in the choice of the sign in (16) that has to beanalysed carefully. As we have said, in terms of the cos-mic time t , the wave function φ + represents a contract-ing universe and φ − an expanding universe [see, (12)]. Inthat case, in order for the WKB-time (16) to representthe cosmic time t , we have to choose the variable t − inthe branch φ − , so that ∂a∂t − = 1 a ∂S∂a > , (19)represents an expanding universe; and for the contractingbranch represented by φ + we must choose t + , so that ∂a∂t + = − a ∂S∂a < , (20)describes a contracting universe. With this choice, theequation (18) reads, i (cid:126) ∂∂t ± ψ ± ( t ± , ϕ ) = ˆ H m ψ ± ( t ± , ϕ ) , (21)where, ψ ± ( t ± , ϕ ) ≡ ψ ± [ a ( t ± ) , ϕ ], evaluated in the solu-tions of the background given by (19) and (20). There-fore, we have ended up with two universes, one con-tracting and another expanding, both filled with matter,which is the customary interpretation (see, Fig. 1).We can make however a different interpretation. Itcan be assumed that the physical time variable, i.e. thetime variable measured by actual clocks that are eventu-ally made of matter, is the time variable that appears inthe Schr¨odinger equation of the observer’s physical ex-periments. In that case, it is worth noticing that thephysical time variable of observers in the two universesis reversely related, t + = − t − . For instance, let us con-sider t − as the physical time . Then, in terms of thetime variable t − the evolution of the scale factor is givenby (19) so the two wave functions, φ + and φ − , represent We are then assuming the time measured by one particular ob-server.
FIG. 1. The contracting and the expanding branches of aDeSitter spacetime, both filled with matter.FIG. 2. In terms of the internal time t − the two branches canbe interpreted as expanding universes, one of them filled withmatter and the other filled with antimatter. both an expanding universe. However, in terms of t − theSchr¨odinger equation (18) becomes, i (cid:126) ∂∂t − ψ − ( t − , ϕ ) = ˆ H m ψ − ( t − , ϕ ) , (22)for the wave function ψ − , and − i (cid:126) ∂∂t − ψ + ( t − , ϕ ) = ˆ H m ψ + ( t − , ϕ ) , (23)for the wave function ψ + . The ’wrong sign’ in (23) isnot problematic [3]. It only indicates that (23) is theSchr¨odinger equation of the complex conjugated wavefunction ψ ∗ + with a CP -transformed Hamiltonian [3]. Itis therefore the Schr¨odinger equation of the conjugatedfield that represents the antimatter of ϕ . In this case,we have ended up with the description of two expandinguniverses, one of them filled with matter and the otherfilled with antimatter (see, Fig. 2).The two interpretations can be graphically sketched asin Fig. 3. It clearly resembles the interpretation of par-ticles and antiparticles in a quantum field theory of mat-ter fields (e.g. QED). The analogy can be taken furtherand the creation of the universe can be more appropri-ately described in the field theoretical approach called third quantisation [18–21], where the wave function ofthe universe can be seen as a field that propagates in thesuperspace, in which the time like variable is the volumeof the universes . Therefore, the positive and negativefrequency modes (the ’particles’ and ’antiparticles’) canbe associated with expanding and contracting universes,or following an interpretation more consistent with thefield theoretical approach they can be interpreted as ex-panding universe-antiuniverse pairs (see, Fig. 2). IV. OBSERVATIONAL IMPRINTS
One of the most interesting properties of the creation ofthe universe in universe-antiuniverse pairs is that besidesrestoring the matter-antimatter asymmetry apparentlyperceived from the point of one of the single universes,it might provide us as well with observational imprintsin the properties of a universe like ours originated in theentanglement of the matter and antimatter fields of thetwo universes. The quantum field theory of the matterfield in the two universes would follow the customaryapproach and can be expanded in Fourier modes as usual, ϕ ( x, t ) = 1 √ (cid:88) n F n ( x ) v ∗ n ( t ) ˆ a n + F ∗ n ( x ) v n ( t ) ˆ b †− n . (24)The only difference with respect to the development ina single universe is that now the particles (ˆ a n ) and theantiparticles (ˆ b n ) would live (propagate) in different butcorrelated universes. In a time evolving spacetime thereis a generation of particles along the evolution of theuniverse because the invariant representations, ˆ a n andˆ b n , do not coincide with the diagonal representation ofthe Hamiltonian at any given time. Both representa-tions, the invariant and the instantaneously diagonal rep-resentation, are related by a Bogolyubov transformation.However, in the case of a universe-antiuniverse pair, dueto the common origin, one can assume that the modesof the two universes are entangled so the Bogolyubovtransformation would then read [11]ˆ a n = µ ( t ) ˆ c n − ν ∗ ( t ) ˆ d †− n (25)ˆ b n = µ ( t ) ˆ d n − ν ∗ ( t ) ˆ c †− n , (26)where µ ( t ) and ν ( t ) are two functions that for simplicitywe omit here (see, Ref. [11] for the details). In that case,the composite vacuum state of the invariant representa-tion, | a b (cid:105) , would be full of particles and antiparticlesthat would live in disconnected universes so they wouldnot annihilate each other. The full theoretical description of the wave function ˆ φ will bepublished soon. This can also be seen as a plausible boundary condition.
FIG. 3. In analogy to the creation of particle-antiparticlepairs in a quantum field theory, a contracting and an ex-panding pair of universes can be interpreted as an expandinguniverse-antiuniverse pair in the third quantisation formal-ism.
The quantum state of the matter field in one of thetwo universes would be given by the density matrix thatis obtained by tracing out from the composite vacuumstate, ρ = | a b (cid:105)(cid:104) a b | , the degrees of freedom of thepartner universe, i.e. [11] ρ = Tr ρ = (cid:89) n Z n ∞ (cid:88) N =0 e − T ( N +1 / | N c, n (cid:105)(cid:104) N c, n | , (27)where | N c, n (cid:105) are the number states of the diagonal rep-resentation in one of the universes, Z n is the partitionfunction, and T ≡ T n ( t ) = 1ln(1 + | ν | ) . (28)The quantum state (27) is a very specific state so in prin-ciple one should expect some distinguishable imprintsfrom it. Let us notice that it is not exactly a thermalstate for two reasons. First, the temperature of entangle-ment T is time dependent ; and second and more impor-tant, it depends on the value of the mode, i.e. the modeshave not thermalised in (27) so we cannot properly talkabout a thermal state. In fact, it can be shown [11] that T n → n (cid:29)
1) meaning that the lo-cal particles of the field do not feel the inter-universalentanglement; only the modes with wavelengths of or-der of the Hubble distance are significantly affected. Thequasi thermal character of the quantum state (27) is a This is however not an important departure from the thermalstate in the sense that at any given time the number of particlesof the matter field follows a thermal distribution very specific prediction of the creation of the universe ina universe-antiuniverse pair.With the quantum state (27) one can compute all theassociated thermodynamical magnitudes. For instance,the energy of the state (27) is E = Trˆ ρ ˆ H = ω n (cid:0) | µ n | + | ν n | (cid:1) , (29)which in the case of a flat DeSitter spacetime produces abackreaction energy density given by [11] ε = H (cid:26) − m H log b H + (cid:18) m H (cid:19) (cid:18) − b H (cid:19)(cid:27) , (30)where b is an infrared cutoff. However, it turns out thatthis energy is the same that the one produced by thebackreaction of the superhorizon modes of the field inthe single universe scenario (see [22, 23]). Therefore, itis an observable imprint of the creation of universes inpairs but it is not a distinguishable one.A distinguishable imprint may come from the spectrumof fluctuations of the matter field. In the customary sce-nario of a single universe it is typically given by [24] δφ n = H √ π x (cid:0) J q ( x ) + Y q ( x ) (cid:1) , (31)where, x ≡ nHa = n ph H ∼ H − L ph . (32)However, if the initial state of the inhomogeneities isgiven by the quasi-thermal state (27), then [11] (cid:104)| φ n | (cid:105) = 1 M ω n ( | ν | + 12 ) , (33)and the spectrum of fluctuations, which is given by δφ n = n π ∆ φ n , (34)with (∆ φ n ) = (cid:104)| φ n | (cid:105) − |(cid:104) φ n (cid:105)| . (35)can be related to the spectrum of fluctuations in the sin-gle universe scenario by [11] δφ eu n δφ su n = (cid:118)(cid:117)(cid:117)(cid:116) (cid:32) x (1 + x )(1 + m H x ) (cid:33) , (36)where the superscripts ’ eu ’ and ’ su ’ refer to the entan-gled universe and the single universe scenarios, respec-tively. Let us first notice that the large modes ( x (cid:29) δφ th n ≈ δφ I n , as ex-pected (large modes do not feel the inter-universal en-tanglement). However, the departure may be significant for the horizon modes, x ∼
1. This is a distinctive effectof the creation of the universes in entangled universe-antiuniverse pairs and it should leave, at least in princi-ple, an observable imprint in the properties of the CMB.It has no analogue in the context of an isolated universeand therefore it is a distinguishable effect of the creationof universes in pairs that, incidentally, would make falsi-fiable the whole multiverse proposal.
V. CONCLUSIONS
The creation of a contracting and an expanding pairof universes can be interpreted as the creation of a pairof expanding universes, one filled with matter (the ob-server’s universe) and the other filled with antimatter(the partner universe). It can therefore be seen as thecreation of a universe-antiuniverse pair, restoring the ap-parent matter-antimatter asymmetry observed from thepoint of view of the single universes. It is worth notic-ing that the creation of a universe-antiuniverse pair isnot necessarily a mechanism for producing the matter-antimatter asymmetry observed in our universe becausethe particles and antiparticles of the original inflaton fieldwould eventually decay indistinguishable into the parti-cles and antiparticles of the standard model (SM) follow-ing the symmetric decays of the SM, so in general westill need a mechanism for producing the baryon asym-metry. However, the creation of universes in universe-antiuniverse pairs does restore the asymmetry becausefrom the global point of view of the two universes thetotal amount of matter is completely balanced with theamount of antimatter, i.e. whatever is the mechanismproducing the baryon asymmetry in one of the universesa parallel mechanism should be producing the antibaryonasymmetry in the partner antiuniverse.One can also claim that in a multiverse made up ofuniverse-antiuniverse pairs there would be a distributionof universes with different amounts of matter and an-timatter, which would be completely balanced howeverwith the amount of antimatter and matter of their part-ner antiuniverses. In some of these universes the amountof matter and antimatter in each single universe wouldbe balanced too so they would annihilate and these uni-verses would be only full of radiation. These would beperhaps the majority of universes. However, in some uni-verses, due to quantum fluctuations, the amount of mat-ter might slightly exceed the amount of antimatter andthose would be the only universes in which galaxies andhuman being can be produced, being still fully satisfiedthe matter-antimatter symmetry in the whole multiverse.We would be just living in one of these universes . I would like to thank M. Dabrowski for suggesting the anthropicversion of the matter-antimatter asymmetry produced in a mul-tiverse made up of entangled universe-antiuniverse pairs.
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