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Is dark matter made of mirror matter? Evidence from cosmological data. Paolo Ciarcelluti∗ Web Institute of Physics, www.wiph.org Quentin Wallemacq† IFPA, Dép. AGO, Université de Liège, 4000 Liège, Belgium (Dated: November26, 2012) Wepresentnewfastnumericalsimulationsofcosmicmicrowavebackgroundandlargescalestruc- turein thecase in which thecosmological dark matter is made entirely or partly of mirror matter. 2 Weconsiderscalar adiabatic primordialperturbationsatlinearscales inaflatUniverse. Thespeed 1 ofthesimulationsallowsusforthefirsttimetouseMarkovChainMonteCarloanalysestoconstrain 0 themirrorparameters. AUniversewithpuremirrormattercanfitverywelltheobservations,equiv- 2 alentlytothecaseof anadmixturewith cold darkmatter. Inboth cases, theanalyses showaclear v indication of the presence of a consistent amount of mirror dark matter, 0.05.Ωmirrorh2 .0.12. o N PACSnumbers: 98.80.-k,95.35.+d,98.70.Vc,98.65.Dx Keywords: cosmology,cosmicmicrowavebackground, largescalestructure,darkmatter 2 2 The existence of dark matter in the Universe seems to particles have left-handed interactions, mirror particles ] be an unavoidable evidence, as confirmed by all the cur- have right-handed interactions [11]. Thus, they are sta- O rentlyavailableastrophysicalobservationsatscalesrang- ble exactly as their ordinary counterparts. C ing from cosmological to galactic. At the same time, its The ordinary and mirror particles have the same . nature is still completely unknown, and is limited to its massesandobeytothesamephysicallaws,butthethree h qualitative behaviour for the process of structure forma- non-gravitational interactions act on ordinary and mir- p - tion. TogetherwithBigBangnucleosynthesis(BBN),the ror sectors completely separately, the only link between o most powerful cosmological tests for dark matter candi- all of them being the gravity. Since mirror baryons do r t dates are the cosmic microwave background (CMB) and not interact with photons, or interact only very weakly, s large scale structure (LSS) power spectra, with their in- the presence of mirror matter is felt mainly by its grav- a [ creasing precisions due to the huge observational efforts itational effects, which is exactly the definition of “dark of severalgroups. matter”. 1 PreviousanalyticalandnumericalstudiesonCMBand Hence mirror matter is a stable self-interacting1 dark v LSSpowerspectra[1–6]haveonlylimitedthe parameter matter candidate that emerges if one, instead of (or in 4 5 space of mirror dark matter, without providing a defini- addition to) assuming a symmetry between bosons and 3 tive cosmologicalanswerto its existence. Here we finally fermions(supersymmetry),assumesthatnatureisparity 5 address this question. symmetric. 1. As suggested many years ago by Lee and Yang [7], Besidesbeingaviableandpowerfulcandidatefordark 1 to suppose the existence of mirror matter is the sim- matter,theincreasinginterestonmirrormatterisdueto 2 plest way to restore the parity symmetry of the laws thefactthatitprovidesoneofthefewpotentialexplana- 1 of nature. Their idea was later developed by other au- tionsfortherecentDAMAannualmodulationsignal[15], v: thors [8–11], and a lot of studies were devoted to it, together with the results of other direct detection exper- i showing its compatibility with all the available experiments (CDMS, CoGeNT, CRESST,XENON) [16]. The X imental and observational constraints (for reviews, see compatibility of this scenario with BBN constraints has r Refs. [3, 12–14]). In some cases, as the results of direct already been studied [19, 20]. a detectionexperiments[15,16]ortheobservationsofneu- Given its consistency with experiments and observa- tronstars[17,18],thereareinterestingsuggestionsofthe tions, and the unfruitful attempts to prove the existence existence of mirror matter. of the other dark matter candidates, scientific commu- Theoriginalideawastohaveaparallelhidden(mirror) nity is facing an emergent question: “is mirror matter sector of particles which is an exact duplicate of the ob- the dark matter of the Universe (or at least a significant servable sector. In the modern context of gauge theories partofit)?” Onepossibilitytoanswerthisquestionisto thisimpliestheexistenceofanexactparity(mirror)sym- look at the cosmologicalsignatures of mirror particles. metrybetweentwoparticlesectors,thataredescribedby Itisworthwhiletonotethatthepresenceofthemirror the same Lagrangianand coupling constants, andconse- quently have the same microphysics,but where ordinary 1 Astrophysical constraints on self interactions of dark matter presentinliteraturearevalidonlyforhomogeneousdistributions ∗ [email protected] ofdarkmatterparticles,andarethereforenotdirectlyapplicable † [email protected] tothemirrormattercase. 2 sectordoesnotintroduceanynewparametersinparticle photon-baryon equipartitions z and z′ . The MRE bγ bγ physics(ifweneglectthepossibleweaknon-gravitational occurs at the redshift interactionsbetweenvisibleandhiddensectors). Butthe Ω Ω h2 factthatmicrophysicsisthesameinordinaryandmirror 1+z = m ≈2.4·104 m , (3) sectors does not mean that also macroscopicrealizations eq Ωr 1+x4 should be the same. The different macrophysics is usu- which is always smaller than the value obtained for an ally parametrized in terms of only two “cosmological” ordinary Universe. The MRD takes place in every sec- free parameters: the ratio x of temperatures of the two tor only after mostelectronsand protonsrecombineinto sectors, in terms of temperatures of the ordinary and neutral hydrogen and the free electron number density mirror photons in the cosmic background radiation; the diminishes, so that the interaction rate of the photons relativeamountβ ofmirrorbaryonscomparedto the or- drops below the Hubble expansion rate. Since T′ ≃ dinary ones. dec T up to small corrections, we obtain dec x≡ S′ 1/3 ≃ T′ and β ≡ Ω′b , (1) 1+zd′ec ≃x−1(1+zdec), (4) (cid:18)S (cid:19) T Ω b sothatthe MRD inthe mirrorsectoroccursearlierthan where T (T′), Ωb (Ω′b), and S (S′) are respectively inthe ordinaryone. Ithasbeenshown[2,12]that, com- the ordinary (mirror) photon temperature, cosmologi- paringEqs.(3)and(4),forxsmallerthanatypicalvalue cal baryon density (normalized, as usual, to the critical x themirrorphotonswoulddecoupleyetduringthera- eq density of the Universe), and entropy per comoving vol- diation dominated period, and the evolution of primor- ume [12]. dialperturbationsinthelinearregimeispracticallyiden- The present energy density contains relativistic (ra- ticaltothestandardcolddarkmatter(CDM)case. Also diation) component Ωr, non-relativistic (matter) com- the photon-baryon equipartition happens in the mirror ponent Ωm and the vacuum energy (cosmological term sector earlier than in the ordinary one, according to the or dark energy) density ΩΛ. According to the infla- relation tionary paradigm the Universe should be almost flat, Ω′ Ω β β Ωretsoutlt=s oΩnmth+eΩCrM+BΩaΛnis≈ot1ro,pwy.hiNchowagbroetehs rwaedlliawtiiotnhatnhde 1+zb′γ = Ω′γb ≃ Ωγbx4 =(1+zbγ)x4 >1+zbγ . (5) mattercomponentscontainthemirrorcomponents2,and PreviousanalyticalandnumericalstudiesonCMBand the matter composition of the Universe is expressed in LSS power spectra [1–6, 22] have only shown, using a general by qualitative comparison with observations, that: (i) for Ω =Ω +Ω′ +Ω =Ω (1+β)+Ω , (2) low values of mirror temperatures (x.0.3) all the dark m b b DM b DM mattercanbemadeofmirrorbaryons;(ii)forhighvalues (x&0.3)mirrorbaryonscanbe presentasanadmixture where the term Ω includes the contributions of any DM other possible dark matter particles but mirror baryons. with CDM. At the time of BBN the mirror photons γ′, electrons Now we are finally able to fit the cosmologicalparam- e±′ andneutrinosν′ wouldgivea contributionto the eters and obtain their quantitative estimates. e,µ,τ energetic degrees of freedom equivalent to an effective number of extra neutrino families ∆N ≃ 6.14x4. Cur- ν TABLE I. Adopted flat priors for theparameters. rentestimatesof∆N [21]correspondtoanupperbound ν x.0.7,andhenceatthenucleosynthesisepochthetem- parameter lower limit upperlimit peratureofthemirrorsectorshouldbesmallerthanthat Ωbh2 0.01 0.1 of the ordinary one, T′ <T. Ωcdmh2 0.01 0.8 x 0.05 0.7 Duetothetemperaturedifferencebetweenthetwosec- β 0.5 9.0 tors, the cosmological key epochs take place at different 100 θs 0.1 10 redshifts, and in particular they happen in the mirror τ 0.01 0.8 sector before than in the ordinary one [2, 12]. The rel- ns 0.7 1.3 evant epochs for the cosmic structure formation are re- ln(1010As) 2.7 4 lated to the matter-radiation equality (MRE) z , the eq matter-radiation decouplings (MRD) z and z′ due dec dec to the plasma recombinations in both sectors, and the We have modified the publicly available cosmological simulation tools CAMB [23] and CosmoMC [24] in order to include the effects of mirror matter. Since the physics of the mirror particles is the same as our parti- 2 Since mirror parity doubles all the ordinary particles, even if cles, we have doubled the equations separately in each theyare“dark”(i.e.,wearenotabletodetectthemnow),what- sector, and considered all the particles when describing evertheformofdarkmattermadebysomeexoticordinarypar- the gravitational interactions. The recombinations are ticles,therewillexistamirrorcounterpart. computedseparatelyfor eachsector. The computational 3 TABLE II. 1-σ constraints on theparameters obtained using different dark matter compositions and cosmological tests. parameter standard mirror mirror mirror+CDM mirror+CDM CMB CMB+LSS CMB CMB+LSS primary Ωbh2 0.02218±0.00053 0.02184±0.00069 0.02188±0.00045 0.02226±0.00058 0.02184±0.00053 Ωcdmh2 0.1157±0.0036 0 0 0.055±0.016 0.0661±0.0062 ns 0.961±0.013 0.952±0.019 0.950±0.011 0.969±0.015 0.951±0.013 ln(1010As) 3.088±0.032 3.105±0.035 3.099±0.032 3.114±0.044 3.099±0.031 100θs 1.0382±0.0026 1.0376±0.0036 1.0363±0.0026 1.0403±0.0035 1.0366±0.0028 τ 0.084±0.014 0.080±0.014 0.079±0.013 0.086±0.014 0.079±0.013 mirror x – 0.29±0.10 0.180±0.030 0.39±0.11 0.170±0.034 β – 5.75±0.33 5.62±0.11 3.14±0.71 2.61±0.15 derived Ωm 0.295±0.020 0.345±0.041 0.343±0.016 0.312±0.042 0.344±0.034 ΩΛ 0.705±0.020 0.655±0.041 0.657±0.016 0.688±0.042 0.656±0.034 zre 10.4±1.2 10.3±1.3 10.3±1.2 10.8±1.2 10.2±1.2 h 0.685±0.016 0.656±0.032 0.650±0.011 0.690±0.025 0.651±0.023 age [Gyr] 13.84±0.12 13.84±0.25 13.95±0.11 13.56±0.25 13.95±0.13 σ8 0.827±0.022 – 0.830±0.028 – 0.834±0.034 times of this modified version of CAMB are consider- N =3.046. eff ablyincreased,butstillfastenoughtocomputethemany We consider two different chemical compositions of models neededfor a Monte Carlofitin reasonabletimes. dark matter: the case pure mirror and the case mixed Compared with previous numerical simulations [1– mirror-CDM.Inaddition,weperformanalysesusingtwo 5], we have used an updated estimate of the primor- different configurations: the CMB only and the CMB dial chemical composition of mirror particles present in combined with the LSS. The CMB dataset is provided Refs. [12, 25–28], and a more accurate treatment of the by the WMAP7 team [30], which measured the acous- recombinationsofordinaryandmirrorparticlesusingthe tic oscillations of the primordial plasma on degree scales numerical code RECFAST [29]. The new models based with cosmic-variance-limited precision. For the LSS, in- on CAMB and the more accurate treatment of mirror stead,weincludethepowerspectrumextractedfromthe BBN are consistent with the previous ones, but there is SDSS-DR7 luminous red galaxy sample [31] limited to a strong improvement of the computational time, allow- the length scales larger than k ∼ 0.2hMpc−1 to avoid ing us now to constrain the parameters. non-linear clustering and scale-dependent galaxybiasing We use a Markov Chain Monte Carlo (MCMC) sam- effects. Forcomparison,werunalsoaMCMCchainfora pling ofthe multi-dimensionallikelihoodasa functionof standard ΛCDM cosmology, with the same assumptions model parameters, based on the computations of CMB and priors, to use as a reference model. The results of and LSS power spectra obtained with our modified ver- therunsareshowninTableII,wheretheestimatesofthe sion of CAMB. parametersandthe1-σ confidenceintervalsareobtained We sample the following eight-dimensional set of cos- by marginalizingthe multi-dimensionallikelihoods down mological parameters, adopting flat priors on them with to one dimension. The correspondingbest-fit models are broaddistributions, as shownin Table I: the baryonand shown in Figs. 1 and 2. colddarkmatterdensitiesΩ h2 andΩ h2,therelative Looking at Table II, we see that the values of the pri- b cdm mirrorphotontemperaturex, the relativemirrorbaryon mary cosmological parameters, except obviously for the density β, the ratio of the sound horizon to the angular CDMdensity,donotvarysignificantlybetweenthestan- diameter distance at decoupling θ , the reionization op- dardmodel andboth the pure andmixedmirrorcompo- s tical depth τ, the scalarspectral index n and the scalar sitions,forbothkindsofanalysis(CMBandCMB+LSS). s fluctuationamplitude A . The upper limit onxis setby Going to the derived parameters, there is an increase of s the aforementioned BBN limit. In addition, we obtain themattercontentoftheUniverseattheexpensesofthe constraints on derived parameters: the matter and dark darkenergy. Thisispartlyduetoabiggermatterdensity, energydensitiesnormalizedtothecriticaldensityΩ and andpartlytothedecreaseoftheHubbleparameter,that m Ω , the reionization redshift z , the Hubble parameter is anywaycompatible withthe currentestimates. Forall λ re h, the age of the Universe in Gyr, the density fluctua- the models, the non-baryonic matter density is between tion amplitude σ at 8h−1Mpc. The runs also include 5 and 6 times the baryonic density, in accordance with 8 weak priors on the Hubble parameter, 0.4 ≤ h ≤ 1.0, commoncosmologicalanalyses. Butthemostinteresting and on the age of the universe, 10 ≤ age(Gyr) ≤ 20. In result is concentrated in the lines constraining the mir- all the computations we assume scalar adiabatic initial ror parameters. Concerning x, the CMB only analysis conditions in a flat Universe (Ω = 1), a dark energy estimates a pure mirror model with x≃0.3, around the tot equation of state with w = −1, massless neutrinos, and preferred values able to explain the dark matter direct the number of neutrino families of the standard model detection experiments [15, 16], while for mixed mirror 4 6000 6000 WMAP 7 WMAP 7 standard standard 5000 mirror (CMB) 5000 mirror+CDM (CMB) mirror (CMB+LSS) mirror+CDM (CMB+LSS) 2K) 4000 2K) 4000 µ µ π ( π ( / 2Cl 3000 / 2Cl 3000 1) 1) + + l(l 2000 l(l 2000 1000 1000 0 200 400 600 800 1000 1200 0 200 400 600 800 1000 1200 multipole moment l multipole moment l SDSS LRG DR7 SDSS LRG DR7 3) 3) c c p 10000 p 10000 M M 3 (h 3 (h k) k) P( P( 0.1 0.1 k/h (Mpc-1) k/h (Mpc-1) FIG.1. CMBandLSSpowerspectraforbest-fitmodelswith FIG. 2. As in Fig. 1, but for models with baryons, mirror baryonsandmirrormatterobtainedusingCMBonly(dotted matter, and cold dark matter. line) or both CMB and LSS (dashed line). For comparison we show also the standard model fit (solid line). reference standard model. For the CMB the models ob- this value is even bigger, around x ≃ 0.4. The inclusion tained fitting both CMB and LSS data are almost indis- of the LSS lowers significantly these values at x ≃ 0.18 tinguishable, and few differences are present in the LSS for both pure and mixed mirror, confirming the higher powerspectra. The exceptions arethe models computed sensitivity of the LSS on x already evidenced in previ- using CMB only, for which the high values obtained for ous works[1, 12]. We finally look at the most significant x compromise, as expected, their compatibility with the parameter, β, which expresses how much, if any, mirror matter power spectrum. matterispresentintheUniverse. Inthiscasetheresults obtained using CMB alone or combined with the LSS Tosummarize,inthisworkwehaveobtainedtwomain are similar. For pure mirror this value is between 5.5 results. Firstof all,for the firsttime the twoparameters and 6, clearly showing that cosmology requires a strong describing the mirror matter are constrained. Consid- presence of mirror matter in order to interpret its ob- ering the most stringent analyses performed using both servables. IncaseofmirrormixedwithCDM,theresults the CMB and LSS, we obtained x = 0.180±0.030 and showsimilardensitiesofmirrormatterandCDM.Thisis β = 5.62±0.11 for pure mirror, x = 0.170±0.034 and averyinterestingresult,sinceitmeansthat,whenitcan β = 2.61 ± 0.15 for mixed mirror-CDM. These values freely choose between mirror dark matter or collisionless lie in the range required for interesting consequences on massive WIMPs, cosmology unequivocally requires the observations and experiments. 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