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Antimatter from the Cosmological Baryogenesis and the Anisotropies

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Antimatter from the Cosmological Baryogenesis and the Anisotropies Antimatter from the cosmological baryogenesis and the anisotropies and polarization of the CMB radiation Pavel D. Naselsky1,2,3, Lung-Yih Chiang1 1Theoretical Astrophysics Center, Juliane Maries Vej 30, 2100 Copenhagen, Ø Denmark 2Niels Bohr Institute, Juliane Maries Vej 30, 2100 Copenhagen, Ø Denmark 3Rostov State University, Zorge 5, 344090 Rostov-Don, Russia We discuss the hypotheses that cosmological baryon asymmetry and entropy were produced in the early Universe by phase transition of the scalar fields in the framework of spontaneous baryoge- nesis scenario. We show that annihilation of the matter-antimatter clouds during the cosmological hydrogen recombination could distort of the CMB anisotropies and polarization by delay of the recombination. After recombination the annihilation of the antibaryonic clouds (ABC) and bary- onic matter can produce peak-like reionization at the high redshifts before formation of quasars and early galaxy formation. We discuss the constraints on the parameters of spontaneous baryogenesis scenario by the recent WMAP CMB anisotropy and polarization data and on possible manifestation of the antimatter clouds in the upcoming Planck data. INTRODUCTION possible late reionization of the hydrogen by the product of annihilation and the corresponding transformation of the CMB anisotropy and polarization power spectrum Recent release of the first-year WMAP data has con- taking into account present WMAP and CBI observa- firmed that our Universe is non-baryonic dominated. The tional data. Finally we will show that the upcoming vast collection of stars, galaxies and clusters neverthe- Planck mission will be able to detect corresponding man- less contains a huge amount of baryons without strong ifestation of matter -antimatter annihilation even if the evidence of antibaryon contamination to the spectrum well-known Sunyaev-Zeldovich y-parameter would be one of electromagnetic radiation in the Universe. Does it order of magnitude smaller that the COBE FIRAS limit mean that starting from the baryogenesis epoch all an- [7, 8, 9]. tibaryons, or more generally speaking, antimatter anni- hilate with the baryonic matter producing radiation and only relatively small amount of antibaryons can survive BARYON-ANTIBARYON BUBBLE FORMATION up to the present day during the expansion of the Uni- IN THE UNIVERSE verse? The answer to this question has been the point of discussions in the literature (see for review in [1, 2, 3, 4]) It is assumed [1] that scalar baryon of SUSY model ξ including the Big Bang Nucleosynthesis properties, an- is coupled to the scalar inflaton field Φ by the following tiprotons in the vicinity of the Earth and so on. The aim potential of this paper is to investigate antimatter contamination in the recent CMB data, namely, the WMAP anisotropy V (ξ, Φ)=(λξ2 + h.c.)(Φ Φ )2, (1) and polarization data through distortions of the hydro- int − crit gen recombination kinetics and possible late reionization where λ is the coupling constant and Φcrit is some critical arXiv:astro-ph/0312168v2 20 Mar 2004 of the plasma and make the corresponding prediction for value of the Φ field, which determines the point of mini- the future Planck mission. mum of the Vint(ξ, Φ) potential. Starting from the high We re-examine the baryogenesis models following the values Φ Φ the inflaton field decreases down to int ≫ crit arguments by [1], in which the baryonic and antibaryonic Φcrit and Vin(ξ, Φ) potential reach the point of minimum, matter are very non-uniformly distributed at very small while at Φ Φcrit for Vint(ξ, Φ) potential we will have ≪ 2 2 scales (for example, the corresponding mass scale can be Vint(ξ, Φ) = (λξ + h.c.)Φcrit = V (ξ) independently on 3 5 equivalent to M 10 10 M⊙ [1] and follows the adi- the properties of the Φ field. It has been shown [1, 2] that abatic perturbation∼ upon− these scales. Obviously, the because of the properties of the interactions the most fa- possibility of having non-uniformly distributed baryonic vorable conditions for baryogenesis might be created only fraction of the matter at very small scales is related to the for a short time scale. It corresponds to a relatively small Affleck-Dine baryogenesis [5] or the spontaneous baryo- spatial scales. Thus, the general picture of the baryonic genesis mechanism [6]. Taking into account the electro- matter-antimatter spatial distribution would be similar magnetic cascades driven by proton-antiproton annihi- to random distribution of the islands with high baryon lation at the epoch of hydrogen recombination, we will (or anti-baryon) asymmetry floating in the the normal show how they distort the kinetics of the recombination matter with β = n /n 5 10−10, where n and cmb b ≃ × cmb producing corresponding features in the CMB anisotropy nb are the present number densities of the CMB pho- and polarization power spectrum. Then we will discuss tons and baryons. The mass distribution function of the 2 baryon (anti-baryon) clouds (ABC) is also estimated [1] a form of primordial anti-baryonic clouds. Let us de- scribe the dynamics of such ABC evaporation in the hot dn M exp γ2 ln2 (2) plasma. For simplicity we will further assume that a sin- dM ∝ − Mcrit gle ABC has spherically symmetric density distribution (ρ ρ (r)) with the characteristic scale R starting where γ and Mcrit are free parameters of the theory. As in ≡ in one can see from Eq.(2), if γ 1 then the mass spec- from which the contact between ABC and the outer bary- trum is localized at M M ,≫ while for γ 1 the mass onic matter leads to energy release due to annihilation ∼ crit ∼ spectrum will have monotonic character for the clouds 1 2 distribution over wide range of masses. Dolgov and Silk dE 2 2 3kT =4πR εoutvT =4πR cεout 2 (8) [1] have also pointed out that Mcrit could be close to the dt 2mpc solar mass M⊙, but the range of Mcrit can be naturally 3 5 1/2 ⊙ 2 expanded to 10 10 M [2]. Let us assume that param- where vT = 3kT/2mpc is the speed of sound in the eter γ has especially− high value: γ 1 and the initial ≫ plasma, εoutis the energy density of the outer plasma, distribution function of the baryon-antibaryon clouds is k is the Boltzmann constant, mp is the proton mass and close to the Dirac-δ function: dn/dM δD(M Mcrit) T is the temperature of the outer plasma. Using Eq.(8) ∝ 1/3− 2 and the characteristic size of clouds Rcl Mcrit is much and the energy of the inner ABC matter Ecl = Mcl c ∝ 3 ∼ smaller than the size of the horizon Rrec at the epoch (4πR /3)ηεout for the characteristic time of evaporation 3 of recombination (z 10 ): Rcl Rrec. We denote we get ≃ ≪ ρb,in and ρb,out the anti-baryon density inside and baryon −1/2 density outside the clouds, respectively, and the mean Ecl ηR 3kT density ρ at the scales much greater than R and τev = 2 . (9) b,mean cl ≃ dE/dt 3c 2mpc distances between them, Equation (9) indicates that any clouds with the size −5 −4 −1 1/2 above Rcr (10 10 )η (z/zrec) rh(zrec) will ρb,mean = ρabc,inf + ρb,out(1 f), (3) − survive up to≃ the moment÷ of the cosmological hydrogen 2 −1/2 −3/2 where f is the volume fraction of the clouds. We denote recombination trec 2/3(ΩmH0 ) zrec , where zrec 3 ≃ ∼ ρ 10 is the redshift of the recombination, H0 = 100h is the η = abc,in . (4) ρb,out present value of the Hubble constant, Ωm is the baryonic plus dark matter density scaled to the critical density We can write down the following relations between the and rh(zrec) is the horizon at the moment of recombi- mean value of the density and inner and outer values nation. The baryonic mass at the moment of recom- 19 ηρ bination is in order of magnitude 10 M⊙ [10] and the ρ = b,mean , (5) b,in 1+ f(η 1) corresponding mass scale of the ABC should be roughly 4 7 −3 − (10 10 M⊙)η . If the η parameter is close to unity, and which÷ means that density contrast between the inner and ρ ρ = b,mean . (6) outer zones is small, then the corresponding mass scale of b,out 4 7 1+ f(η 1) the ABC would be 10 10 M⊙. However, if η 10, the − corresponding mass scale÷ of the ABCs could be∼ smaller, Using the functions f and η we can define the anti- 4 and comparable with the scale 10 10 M⊙. baryonic mass fraction ÷ ηf Fb = , (7) 1+ f(η 1) ABC at the nucleosynthesis epoch − which is a function of the characteristic mass scale M0 of the anti-baryonic clouds. Let us compare the characteristic scales of the ABC Obviously, all the parameters f, η and Fb are the re- with a few characteristic scales of process in the frame- sults of the fine tuning of the inflaton Vin(ξ, Φ) leading work of the Big Bang theory. Firstly, the baryonic frac- to the formation of baryonic asymmetry in the Universe. tion of matter and its spatial distribution play a crucial role starting from the epoch when the balance between neutrinos (νe, νe), neutrons (n) and protons (p) in the − + MATTER-ANTIMATTER BARYONIC CLOUDS following reactions n + νe p + e , n + e p + νe, IN THE HOT PLASMA − ↔ ↔ n p + e + νe is broken. The corresponding time scale of→ violation of the neutrino-baryon equilibrium is close At the end of inflation the Universe became radiation- to τνe,p 1 sec when the temperature of the plasma dominated by mostly light products of the inflaton de- was close≃ to T 1010K (see for the review in [11]).
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