arXiv:1211.5354v3 [astro-ph.CO] 20 Jan 2014 unl aetesm irpyis u hr ordinary where but microphysics, conse- same and the constants, have coupling quently and by Lagrangian described are same that the sym- sectors, (mirror) particle two theories exact between gauge an metry ob- of of the existence context the of implies modern duplicate this the exact In an sector. is servable which particles of sector the matter. of mirror suggestions direct interesting of are of existence there neu- results 18], of the [17, observations stars the as tron or cases, 16] it, some [15, see experiments In to detection reviews, exper- 12–14]). devoted (for available [3, were constraints the Refs. observational studies all and au- of with other imental laws lot compatibility by the a its developed of showing sim- later and was the [8–11], idea parity is thors Their the matter nature. restore mirror of to of way existence plest the suppose to finally we Here question. defini- this existence. a its address providing to answer without cosmological matter, parameter tive dark the mirror limited of only have space [1–6] spectra power LSS efforts observational huge groups. in- several the their of to with due spectra, precisions power creasing and (LSS) (CMB) structure background scale microwave candi- large cosmic matter the dark are for dates tests cosmological the powerful (BBN), nucleosynthesis forma- most Bang its structure Big to with of Together limited process tion. is its the time, and for unknown, behaviour same qualitative the completely At still is galactic. nature to cosmological cur- from the rang- ing scales all at by observations confirmed astrophysical available as rently evidence, unavoidable an be ∗ † [email protected] [email protected] h rgnlie a ohv aallhde (mirror) hidden parallel a have to was idea original The [7], Yang and Lee by ago years many suggested As and CMB on studies numerical and analytical Previous to seems Universe the in matter dark of existence The sdr atrmd fmro atr vdnefo cosmolog from Evidence matter? mirror of made matter dark Is ewrs omlg,csi irwv akrud ag s large background, microwave cosmic 98.65.Dx cosmology, 98.70.Vc, Keywords: 95.35.+d, 98.80.-k, numbers: PACS oesetmt h rsneo ossetaon fmirro of amount consistent a dar of cold presence Mar with the admixture use mirro estimate an to pure of models case time with the Universe first to A equivalently the tions, for parameters. made mirror us is the allows matter constrain simulations dark the perturbat cosmological of primordial the speed adiabatic scalar which consider in We case matter. the in ture epeetnwfs ueia iuain fcsi microwa cosmic of simulations numerical fast new present We FA ´p G,Uiested iee 00L`g,Belgiu Li`ege, 4000 Li`ege, Universit´e de AGO, D´ep. IFPA, e nttt fPyis www.wiph.org , of Institute Web Dtd uut2 2018) 2, August (Dated: uni Wallemacq Quentin al Ciarcelluti Paolo oka h omlgclsgaue fmro particles. mirror to of is signatures question cosmological this significant answer the a to at matter least possibility look at One mirror (or it)?” “is Universe of the part question: of commu- matter emergent scientific dark an the candidates, facing matter is existence dark nity the other prove to the attempts of unfruitful the and tions, has 20]. [19, constraints studied BBN been with already scenario The this [16]. of exper- XENON) compatibility detection CRESST, direct CoGeNT, other (CDMS, of iments results [15], the signal explana- with modulation potential together annual few DAMA the recent the of for one to tions provides due it is that matter fact mirror the on interest increasing the matter, parity and in is nature symmetric. (or that between of assumes symmetry (), instead a one, assuming if to) emerges addition that candidate matter “dark of grav- definition its the by exactly mainly matter”. is felt which is weakly, do effects, matter very baryons itational mirror only mirror of interact presence Since or the , . with the interact between being not link them only of the mir- all separately, and completely ordinary three sectors the on ror but act laws, physical interactions same non-gravitational the to obey and masses counterparts. sta- ordinary are their they as Thus, exactly ble [11]. particles interactions mirror right-handed interactions, have left-handed have particles 1 otemro atrcase. app matter directly not mirror therefore the are to and distri particles, homogeneous matter for dark only of valid are literature in present ti otwiet oeta h rsneo h mirror the of presence the that note to worthwhile is It observa- and experiments with consistency its Given dark for candidate powerful and viable a being Besides self-interacting stable a is matter mirror Hence same the have particles mirror and ordinary The srpyia osrit nsl neatoso akmat dark of interactions self on constraints Astrophysical aesrcue akmatter dark structure, cale osa iersae nafltUies.The Universe. flat a in scales linear at ions ∗ atr nbt ae,tecosmological the cases, both In matter. k † akmte,0 matter, dark r atrcnfi eywl h observa- the well very fit can matter r ebcgon n ag cl struc- scale large and background ve o hi ot al nlssto analyses Carlo Monte Chain kov nieyo atymd fmirror of made partly or entirely . 06 m . Ω mirror h cldata. ical 2 . 0 . 12. 1 butions licable dark ter 2

′ sector does not introduce any new parameters in particle -baryon equipartitions zbγ and zbγ. The MRE physics (if we neglect the possible weak non-gravitational occurs at the redshift interactions between visible and hidden sectors). But the Ω Ω h2 fact that microphysics is the same in ordinary and mirror m ≈ · 4 m 1+ zeq = 2.4 10 4 , (3) sectors does not mean that also macroscopic realizations Ωr 1+ x 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 most electrons and protons recombine into 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 relative amount β of mirror baryons compared to the or- drops below the Hubble expansion rate. Since T ′ ≃ dinary ones. dec Tdec up to small corrections, we obtain 1/3 S′ T ′ Ω′ ′ ≃ −1 x ≡ ≃ and β ≡ b , (1) 1+ zdec x (1 + zdec) , (4)  S  T Ωb so that the MRD in the mirror sector occurs earlier than ′ ′ ′ where T (T ), Ωb (Ωb), and S (S ) are respectively in the ordinary one. It has been shown [2, 12] that, com- the ordinary (mirror) photon temperature, cosmologi- paring Eqs. (3) and (4), for x smaller than a typical value cal baryon density (normalized, as usual, to the critical xeq the mirror photons would decouple yet during the ra- density of the Universe), and entropy per comoving vol- diation dominated period, and the evolution of primor- ume [12]. dial perturbations in the linear regime is practically iden- The present energy density contains relativistic (ra- tical to the standard cold (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 ) density ΩΛ. According to the infla- relation tionary paradigm the Universe should be almost flat, ′ Ω Ωb β β Ωtot = Ωm +Ωr +ΩΛ ≈ 1, which agrees well with the ′ b ≃ 1+ zbγ = ′ 4 =(1+ zbγ) 4 > 1+ zbγ . (5) results on the CMB anisotropy. Now both radiation and Ωγ Ωγ x x matter components contain the mirror components2, and the matter composition of the Universe is expressed in Previous analytical and numerical studies on CMB and general by LSS power spectra [1–6, 22] have only shown, using a qualitative comparison with observations, that: (i) for ′ low values of mirror temperatures (x . 0.3) all the dark Ωm =Ωb +Ω +ΩDM =Ωb(1 + β)+ΩDM , (2) b matter can be made of mirror baryons; (ii) for high values x & . where the term ΩDM includes the contributions of any ( 0 3) mirror baryons can be present as an admixture 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 cosmological param- ±′ ′ eters and obtain their quantitative estimates. e and neutrinos νe,µ,τ would give a contribution to the energetic degrees of freedom equivalent to an effective 4 number of extra neutrino families ∆Nν ≃ 6.14 x . Cur- TABLE I. Adopted flat priors for the parameters. rent estimates of ∆Nν [21] correspond to an upper bound parameter lower limit upper limit x . 0.7, and hence at the nucleosynthesis epoch the tem- 2 Ωbh 0.01 0.1 perature of the mirror sector should be smaller than that 2 of the ordinary one, T ′

TABLE II. 1-σ constraints on the parameters obtained using different dark matter compositions and cosmological tests. For the parameter x we reported the upper limit computed at the 95% c.l. parameter standard standard mirror mirror mirror+CDM mirror+CDM CMB CMB+LSS CMB CMB+LSS CMB CMB+LSS primary 2 Ωbh 0.02213 ± 0.00041 0.02205 ± 0.00034 0.02213 ± 0.00040 0.02215 ± 0.00045 0.02225 ± 0.00044 0.02201 ± 0.00034 2 Ωcdmh 0.1113 ± 0.0046 0.1161 ± 0.0031 − − 0.026 ± 0.012 0.036 ± 0.010 ns 0.9616 ± 0.0097 0.9578 ± 0.0081 0.966 ± 0.011 0.961 ± 0.013 0.964 ± 0.012 0.9558 ± 0.0061 10 ln(10 As) 3.051 ± 0.024 3.074 ± 0.021 3.082 ± 0.034 3.090 ± 0.032 3.100 ± 0.038 3.072 ± 0.018 100 θs 1.0406 ± 0.0017 1.0404 ± 0.0015 1.0413 ± 0.0016 1.0403 ± 0.0016 1.0408 ± 0.0017 1.0400 ± 0.0014 τ 0.073 ± 0.012 0.075 ± 0.011 0.083 ± 0.014 0.085 ± 0.016 0.089 ± 0.016 0.0755 ± 0.0085 mirror x − − < 0.456 < 0.297 < 0.479 < 0.315 β − − 5.13 ± 0.30 5.21 ± 0.21 4.03 ± 0.50 3.64 ± 0.46 derived Ωm 0.267 ± 0.025 0.292 ± 0.017 0.273 ± 0.031 0.285 ± 0.020 0.285 ± 0.030 0.291 ± 0.017 ΩΛ 0.733 ± 0.025 0.708 ± 0.017 0.727 ± 0.031 0.715 ± 0.020 0.715 ± 0.030 0.709 ± 0.017 zre 9.3 ± 1.0 9.70 ± 0.95 10.3 ± 1.2 10.5 ± 1.3 10.8 ± 1.4 9.73 ± 0.77 h 0.710 ± 0.022 0.690 ± 0.013 0.708 ± 0.024 0.695 ± 0.017 0.698 ± 0.023 0.690 ± 0.014 age [Gyr] 13.750 ± 0.092 13.793 ± 0.066 13.687 ± 0.093 13.759 ± 0.088 13.71 ± 0.10 13.782 ± 0.067 σ8 − 0.824 ± 0.015 − 0.767 ± 0.021 − 0.746 ± 0.018 times of this modified version of CAMB are consider- all the computations we assume scalar adiabatic initial ably increased, but still fast enough to compute the many conditions in a flat Universe (Ωtot = 1), a dark energy models needed for a Monte Carlo fit in reasonable times. equation of state with w = −1, massless neutrinos, and Compared with previous numerical simulations [1– the number of neutrino families of the standard model 5], we have used an updated estimate of the primor- Neff =3.046. dial chemical composition of mirror particles present in We consider two different chemical compositions of Refs. [12, 25–28], and a more accurate treatment of the dark matter: the case pure mirror and the case mixed recombinations of ordinary and mirror particles using the mirror-CDM. In addition, we perform analyses using two numerical code RECFAST [29]. The new models based different configurations: the CMB only and the CMB on CAMB and the more accurate treatment of mirror combined with the LSS. The CMB datasets are provided BBN are consistent with the previous ones, but there is by the WMAP7 team [30], which measured the acous- a strong improvement of the computational time, allow- tic oscillations of the primordial plasma on degree scales ing us now to constrain the parameters. with cosmic-variance-limited precision, together with the We use a Markov Chain Monte Carlo (MCMC) sam- ACT [31] and SPT [32] observations, which provided pling of the multi-dimensional likelihood as a function of accurate power spectra at higher l’s. For the LSS, in- model parameters, based on the computations of CMB stead, we include the power spectrum extracted from the and LSS power spectra obtained with our modified ver- SDSS-DR7 luminous red galaxy sample [33] limited to sion of CAMB. the length scales larger than k ∼ 0.2h Mpc−1 to avoid We sample the following eight-dimensional set of cos- non-linear clustering and scale-dependent galaxy biasing mological parameters, adopting flat priors on them with effects. For comparison, we run also a MCMC chain for a broad distributions, as shown in Table I: the baryon and standard ΛCDM cosmology, with the same assumptions 2 2 densities Ωbh and Ωcdmh , the relative and priors, to use as a reference model. The results of mirror photon temperature x, the relative mirror baryon the runs are shown in Table II, where the estimates of the density β, the ratio of the sound horizon to the angular parameters and the 1-σ confidence intervals are obtained diameter distance at decoupling θs, the reionization op- by marginalizing the multi-dimensional likelihoods down tical depth τ, the scalar spectral index ns and the scalar to one dimension. For the parameter x, it is just possible fluctuation amplitude As. The upper limit on x is set by to obtain an upper limit, since the probability density of the aforementioned BBN limit. In addition, we obtain that parameter is almost flat in the low-x region, while constraints on derived parameters: the matter and dark it sharply decreases at higher x. We choose to give the energy densities normalized to the critical density Ωm and upper limits at the 95% confidence level. This is compati- Ωλ, the reionization redshift zre, the Hubble parameter ble with what theoretically expected, since, as previously h, the age of the Universe in Gyr, the density fluctua- studied [1, 2, 12], for smaller x the decoupling of mirror −1 tion amplitude σ8 at 8h Mpc. The runs also include baryons happens at earlier times, mimicking more and weak priors on the Hubble parameter, 0.4 ≤ h ≤ 1.0, more the usual CDM behaviour at linear regimes. The and on the age of the universe, 10 ≤ age(Gyr) ≤ 20. In corresponding best-fit models are shown in Figs. 1 and 2 4

6000 WMAP 7 ACT 6000 5000 CMB fits SPT WMAP 7 standard ACT mirror 5000 CMB+LSS fits SPT )

2 mirror+CDM standard

K 4000 mirror µ ) 2 ( mirror+CDM π

K 4000 3000 µ / 2 ( l π 3000 / 2 2000 l l(l+1)C 2000 l(l+1)C 1000

1000 0 500 1000 1500 2000 multipole moment l 0 500 1000 1500 2000 multipole moment l FIG. 1. CMB power spectrum for best-fit models with baryons and mirror matter (dashed line), or baryons, mir- SDSS LRG DR7 ror matter, and cold dark matter (dotted line) obtained using CMB only data. For comparison we show also the standard model fit (solid line). ) 3 10000 (Mpc 3 for analysis based respectively on CMB only and on both

CMB and LSS. P(k) h Looking at Table II, we see that the values of the pri- mary cosmological parameters, except obviously for the CDM density, do not vary significantly between the stan- dard model and both the pure and mixed mirror compo- 0.1 sitions, for both kinds of analysis (CMB and CMB+LSS). k/h (Mpc-1) Going to the derived parameters, there is an increase of the matter content of the Universe at the expenses of the dark energy for models obtained considering the CMB only. This is partly due to a bigger matter density, and FIG. 2. CMB and LSS power spectra for best-fit models with partly to the decrease of the Hubble parameter, that is baryons and mirror matter (dashed line), or baryons, mirror always compatible with the current estimates. For all matter, and cold dark matter (dotted line) obtained using the models, the non-baryonic matter density is between both CMB and LSS datasets. For comparison we show also 5 and 6 times the baryonic density, in accordance with the standard model fit (solid line). common cosmological analyses. But the most interesting result is concentrated in the lines constraining the mirror parameters. Concerning x, the CMB only analysis esti- of a large amount of mirror matter in order to interpret mates at 95% c.l. an upper bound x < 0.456 for a pure its observables. In case of mirror mixed with CDM, the mirror model, while for mixed mirror this bound becomes results show densities of mirror matter that are between slightly weaker, x < 0.479. Both these allowed regions 2 and 4 times larger than those of CDM. This is an in- include the values able to explain the results of the dark teresting result, suggesting that mirror matter could con- matter direct detection experiments [15, 16]. The inclu- tribute significantly to the matter budget of the Universe sion of the LSS significantly tightens the allowed region in a similar way as CDM does. Future data, especially of x for both pure (x < 0.297) and mixed (x < 0.315) on LSS, should help to discriminate between mirror and mirror, confirming the higher sensitivity of the LSS on CDM models. x already evidenced in previous works [1, 12]. Even The likelihoods of the best fit models have very similar these more stringent constraints are compatible with the values for each class of models obtained using CMB only mirror matter interpratation of direct detection experi- or the combination of CMB and LSS data. In the former ments [15, 16]. We finally look at the most significant case, they are − ln(L) = 3772 for pure CDM, − ln(L) = parameter, β, which expresses how much, if any, mirror 3771 for pure mirror and − ln(L) = 3771 for the mixture matter is present in the Universe. The results obtained mirror-CDM, while for the latter they are respectively using CMB alone or combined with the LSS are similar. 3795, 3794 and 3795. Considering the increases of one For pure mirror this value is between 5 and 5.5, show- or two free parameters between the models, these values ing that mirror cosmological models require the presence don’t show statistically significant differences. 5

In Figs. 1 and 2 the agreement of the best fits with Secondly, we have demonstrated that cosmological mod- the data is shown, together with the comparison with els with pure mirror matter, mirror matter mixed with the reference standard model. For the CMB the mod- CDM and pure CDM are equivalent concerning the CMB els obtained in both the analyses, namely fitting CMB and LSS power spectra, as a consequence of the fact that data alone or CMB combined with LSS, are almost in- mirror matter and collisional WIMPs have the same be- distinguishable between themselves, and few differences haviour at linear scales. are present in the LSS power spectra. To summarize, in this work we have obtained two main results. First of all, for the first time the two parameters ACKNOWLEDGMENTS describing the mirror matter are constrained. Consid- ering the most stringent analyses performed using both We are grateful to Jean-R´en´eCudell for useful discus- the CMB and LSS, we obtained x< 0.297 (95% c.l.) and sions, and to an anonymous reviewer for improving the β =5.21±0.21 (1σ) for pure mirror, x< 0.315 (95% c.l.) statistical analysis. PC acknowledges the hospitality of and β =3.64 ± 0.46 (1σ) for mixed mirror-CDM. These the IFPA group and the financial support of the Belgian bounds include the range of parameters required for in- Science Policy during part of this work. QW is supported teresting consequences on observations and experiments. by the Belgian Fund FRS-FNRS as a Research Fellow.

[1] P. Ciarcelluti, Int.J.Mod.Phys. D14, 223 (2005), [18] P. Ciarcelluti and F. Sandin, Phys.Lett. B695, 19 (2011), arXiv:astro-ph/0409633 [astro-ph] arXiv:1005.0857 [astro-ph.HE] [2] P. Ciarcelluti, Int.J.Mod.Phys. D14, 187 (2005), [19] P. Ciarcelluti and R. Foot, Phys.Lett. B679, 278 (2009), arXiv:astro-ph/0409630 [astro-ph] arXiv:0809.4438 [astro-ph] [3] P. Ciarcelluti(2003), arXiv:astro-ph/0312607 [astro-ph] [20] P. Ciarcelluti and R. Foot, Phys.Lett. B690, 462 (2010), [4] Z. Berezhiani, P. Ciarcelluti, D. Comelli, and arXiv:1003.0880 [astro-ph.CO] F. L. Villante, Int.J.Mod.Phys. D14, 107 (2005), [21] Y. Izotov and T. Thuan, Astrophys.J. 710, L67 (2010), arXiv:astro-ph/0312605 [astro-ph] arXiv:1001.4440 [astro-ph.CO] [5] P. Ciarcelluti, Frascati Phys.Ser. 555, 1 (2004), [22] R. Foot(2012), arXiv:1208.6022 [astro-ph.CO] arXiv:astro-ph/0409629 [astro-ph] [23] A. Lewis, A. Challinor, and A. Lasenby, Astrophys. J. [6] A. Y. Ignatiev and R. R. Volkas, Phys. Rev. D68, 023518 538, 473 (2000), astro-ph/9911177 (2003), arXiv:hep-ph/0304260 [24] A. Lewis and S. Bridle, Phys. Rev. D66, 103511 (2002), [7] T. D. Lee and C.-N. Yang, Phys. Rev. 104, 254 (1956) astro-ph/0205436 [8] S. Blinnikov and M. Khlopov, Sov.Astron. 27, 371 (1983) [25] P. Ciarcelluti, AIP Conf.Proc. 1038, 202 (2008), [9] E. W. Kolb, D. Seckel, and M. S. Turner, Nature 314, arXiv:0809.0668 [astro-ph] 415 (1985) [26] P. Ciarcelluti and A. Lepidi, Phys.Rev. D78, 123003 [10] M. Y. Khlopov, G. M. Beskin, N. E. Bochkarev, L. A. (2008), arXiv:0809.0677 [astro-ph] Pustylnik, and S. A. Pustylnik, Sov. Astron. 35, 21 [27] P. Ciarcelluti, AIP Conf.Proc. 1241, 351 (2010), (1991) arXiv:0911.3592 [astro-ph.CO] [11] R. Foot, H. Lew, and R. R. Volkas, Phys. Lett. B272, 67 [28] P. Ciarcelluti(2014), arXiv:1401.2916 [astro-ph.CO] (1991) [29] S. Seager, D. D. Sasselov, and D. Scott, Astrophys.J. [12] P. Ciarcelluti, Int.J.Mod.Phys. D19, 2151 (2010), 523, L1 (1999), arXiv:astro-ph/9909275 [astro-ph] arXiv:1102.5530 [astro-ph.CO] [30] D. Larson, J. Dunkley, G. Hinshaw, E. Komatsu, [13] L. B. Okun, Phys. Usp. 50, 380 (2007), M. Nolta, et al., Astrophys.J.Suppl. 192, 16 (2011), arXiv:hep-ph/0606202 arXiv:1001.4635 [astro-ph.CO] [14] R. Foot, Int.J.Mod.Phys. A19, 3807 (2004), [31] J. L. Sievers, R. A. Hlozek, M. R. Nolta, arXiv:astro-ph/0309330 [astro-ph] V. Acquaviva, G. E. Addison, et al.(2013), [15] R. Foot, Phys.Rev. D78, 043529 (2008), arXiv:1301.0824 [astro-ph.CO] arXiv:0804.4518 [hep-ph] [32] R. Keisler, C. Reichardt, K. Aird, B. Benson, [16] R. Foot, Phys.Rev. D86, 023524 (2012), L. Bleem, et al., Astrophys.J. 743, 28 (2011), arXiv:1203.2387 [hep-ph] arXiv:1105.3182 [astro-ph.CO] [17] F. Sandin and P. Ciarcelluti, Astropart.Phys. 32, 278 [33] B. A. Reid, W. J. Percival, D. J. Eisenstein, L. Verde, (2009), arXiv:0809.2942 [astro-ph] D. N. Spergel, et al., Mon.Not.Roy.Astron.Soc. 404, 60 (2010), arXiv:0907.1659 [astro-ph.CO]