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Home , Baryogenesis, Reionization

arXiv:astro-ph/0312168v2 20 Mar 2004 ntercn M aa aey the namely, contamination data, CMB aim investigate recent The to the on. in is so and paper this the an- of of 4]) properties, vicinity 3, the 2, in Bang tiprotons [1, in Big of review point the for Uni- the including (see the been literature has of the question in expansion this discussions the to answer during The day survive verse? present can the antibaryons to of up amount and small radiation relatively producing only anni- baryonic an- antimatter the all it speaking, with hilate epoch generally Does more the or . from tibaryons, the starting that in mean the radiation strong to electromagnetic without contamination of antibaryon of neverthe- of amount clusters huge evidence and a contains , less of The collection dominated. vast non-baryonic is Universe our that firmed ftepam n aetecrepnigpeito for prediction corresponding future the make the and hydro- late the possible the of and of kinetics distortions recombination through gen data and cls(o xml,tecrepnigms cl a be can scale to corresponding small equivalent the very example, at (for distributed scales non-uniformly antibaryonic very and baryonic are the matter which in [1], by arguments n oaiainpwrsetu.Te ewl discuss will we Then spectrum. power polarization recombination CMB and the the will of in features kinetics we corresponding the recombination, producing distort they of how epoch show annihi- the -antiproton at electro- by lation the driven account cascades into Taking magnetic baryo- [6]. spontaneous mechanism the the genesis to or related [5] is scales baryogenesis small very Affleck-Dine at the matter baryonic the Obviously, of distributed fraction non-uniformly scales. having of these possibility upon perturbation abatic niatrfo h omlgclbroeei n h anis the and baryogenesis cosmological the from Antimatter eetrlaeo h first-year the of release Recent er-xmn h aygnssmdl olwn the following models baryogenesis the re-examine We al aayfrain edsustecntanso h pa the on constraints recent the the r discuss by high We scenario the formation. at reionization th peak-like early of produce anisotropi can CMB matter the onic the recombination of After matter-ant the distort recombination. of could in annihilation fields recombination that scalar hydrogen show the We of transition scenario. phase nesis by Universe early the fteatmte lusi h upcoming the in clouds antimatter the of M edsustehptee htcsooia aynasymmet cosmological that hypotheses the discuss We 1 ∼ hoeia srpyisCne,JlaeMre e 0 21 30, Vej Maries Juliane Center, Astrophysics Theoretical INTRODUCTION mission. 10 3 2 il orIsiue uin aisVj3,20 Copenhage 2100 30, Vej Maries Juliane Institute, Bohr Niels − 10 5 3 M otvSaeUiest,Zre5 400Rso-o,Russia Rostov-Don, 344090 5, Zorge University, State Rostov ⊙ WMAP 1 n olw h adi- the follows and [1] WMAP ae .Naselsky D. Pavel WMAP M nstoyadplrzto aaado osbemanife possible on and data polarization and anisotropy CMB aahscon- has data fteCBradiation CMB the of anisotropy Planck 1 , 2 , 3 data. ugYhChiang Lung-Yih , h M nstoyadplrzto oe spectrum present power account polarization into and taking of anisotropy transformation CMB corresponding the product the the and by annihilation hydrogen the of of reionization late possible fsaino atr-niatranhlto vni the if upcoming even the annihilation Sunyaev-Zeldovich well-known -antimatter that matter show of will ifestation we Finally Planck data. tional 7 ,9]. the 8, that [7, smaller magnitude of order sculdt h clrifltnfil ytefollowing the by Φ field inflaton scalar potential the to coupled is hl tΦ at while V au fteΦfil,wihdtrie h on fmini- of point the determines the which of field, mum Φ the of value where Φ ausΦ values o nibro)aymtyflaigi h h normal the the baryon in high with floating with matter islands anti-baryon) the of (or similar distribution baryonic be random the would to of distribution picture small spatial general relatively the matter-antimatter a Thus, to corresponds scales. It spatial scale. time short only fa- a created most for be the might that baryogenesis interactions 2] for the [1, conditions shown of vorable been properties has the It of field. because Φ the of properties the n osadbros h asdsrbto ucino the of function distribution mass The baryons. and tons AYNATBRO UBEFORMATION BUBBLE BARYON-ANTIBARYON int b crit ti sue 1 htsaa ayno UYmodel SUSY of baryon scalar that [1] assumed is It r h rsn ubrdniiso h M pho- CMB the of densities number present the are ( ξ, and λ niaynccod AC n bary- and (ABC) clouds antibaryonic e )=( = Φ) dhfsbfr omto fqaasand of formation before edshifts iso ilb bet eetcrepnigman- corresponding detect to able be will mission h rmwr fsotnosbaryoge- spontaneous of framework the mte lusdrn h cosmological the during clouds imatter steculn osatadΦ and constant coupling the is int aeeso pnaeu baryogenesis spontaneous of rameters V V sadplrzto ydlyo the of delay by polarization and es in int ≪ ≫ ( V yadetoywr rdcdin produced were and ry β 0Cpnae,ØDenmark Ø Copenhagen, 00 ξ, ( int λξ Φ ξ, Φ = )ptnilrahtepito minimum, of point the reach potential Φ) crit ( 2 crit )=( = Φ) NTEUNIVERSE THE IN ξ, n + 1 cmb )ptnil trigfo h high the from Starting potential. Φ) for h nao eddcessdw to down decreases field inflaton the h.c. ,ØDenmark Ø n, toisadpolarization and otropies /n λξ V )Φ b int 2 ≃ crit 2 + ( ξ, 5 WMAP h.c. = )ptnilw ilhave will we potential Φ) y × prmtrwudb one be would -parameter )(Φ 10 V ( − ξ COBE 10 neednl on independently ) − station and crit where , Φ crit ssm critical some is CBI IA limit FIRAS ) 2 , n observa- cmb and (1) ξ 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 release due to annihilation ∼ crit ∼ spectrum will have monotonic character for the clouds 1 2 distribution over wide range of . 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 , mp is the proton mass and close to the Dirac-δ function: dn/dM δD(M Mcrit) T is the 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 of the recombination, H0 = 100h is the η = abc,in . (4) ρb,out present value of the Hubble constant, Ωm is the baryonic plus 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 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), (n) and (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]). νe,p ≃ cay. Some fraction of matter, however, can exist with The time scale τνe,p determines the characteristic length 3

lνe,p cτνe,p, which in terms of the baryonic mass frac- spectrum distortion in different ways [12, 13]. If τev cor- ≃ −1/2 tion of matter corresponds to responds to the redshift z > 3 105 Ω h2/0.022 × b then we should get a Bose-Einstein spectrum  τνe,p ρb 2 M m 0.15(Ω h )M⊙, −1 νe,p ∼ pl  t  ρ  |t=τνe,p ≃ b n(x, µ) = [exp(x + µ) 1] , (14) pl γ − (10) where x = hν/kT (here h is the , not the where t is the Planck time, ρ and ρ are the densities pl b γ Hubble constant), ν is the frequency of the , µ is of baryons and radiation in the standard cosmological the chemical potential: model without anti-baryonic clouds. Following the SBBN theory we need to specify the moment τ when all light µ = µ exp( 2x /x) (15) end 0 − 0 elements (e.g. He4 and deuterium) were synthesized dur- 2 7/8 ing cosmological cooling of the plasma. This moment is where x0 = 0.018 Ωh /0.125 . It has been shown 2 3 [12] that chemical potential µ is related with the en- in order of the magnitude close to τend 3 10 10  ∼ × ÷ 2 sec. In term of the baryonic mass scale it corresponds to ergy release from annihilation by µ = 3ρabcc /2εr, where εr = 4π/c I(ν)dν and I(ν) is intensity of the CMB. For the redshiftR of annihilation below z = 3 − 3/2 3/2 5 2 1/2 × τend 3 τend 2 10 Ωbh /0.022 the distortions of the CMB power M M 5 10 (Ω h )M⊙. end νe,p 3 b spectrum follows to y-parameter type [14]: ≃ τνe,p  ≃ × 10 sec  (11) 1 exp (ln x +3y ξ2)/4y Thus, if the characteristic mass scale M0 for the baryonic n(x)= dξ − − (16) √4πy Z  exp(ξ) 1  clouds is higher than Mend, the cosmological nucleosyn- − thesis within each cloud and outside the clouds proceeds where independently with others and the mean mass fraction z k(Te Tcmb) dt of each would be the same as in SBBN y = − σT ne(z)c dz (17) Z m c2 dz theory. If all the anti-baryonic clouds will annihilate just 0 e before or after hydrogen recombination epoch , we will and σT is the Thomson cross-section, ne and Te are the have simple renormalization of the baryonic matter den- number density and temperature, respectively. sity at the epoch of nucleosithesis The magnitude of y-distortion is related to the total en- ergy transfer by κ = ∆E/ε = ρ c2/ε = exp(4y) 1. r abc r − ρb + ρabcf At the epoch 103 z 104 the COBE FIRAS data ρ = (12) b,out 1 f give the constraint≤ of the≤ energy release from annihila- − −4 −5 −5 tion κ 2 10 , while y 1.5 10 , and µ0 9 10 where ρb is the present day baryonic density rescaled to at 95%≤ CL× [7, 8, 9]. ≤ × ≤ × the SBBN epoch. As one can see from Eq.(12), if the We would like to point out that the above mentioned fraction of the ABC is small (f 1), then all the devia- ≪ properties of the spectral distortions on the CMB power tion of the light-element mass fractions from the SBBN spectrum is based on the assumption that the distri- predictions would be negligible. bution of the anti-baryonic matter is spatially uniform without any clusterization, and therefore, no additional ENERGY RELEASE TO THE COSMIC PLASMA angular anisotropy and polarization of the CMB would FROM THE ABC AT THE EPOCH OF have been produced during the epoch of hydrogen re- HYDROGEN RECOMBINATION combination. However, cloudy structure of the spatial distribution of anti-matter zones would generate spatial The net of ABC produce the net of the high energy fluctuation of the y-parameters, similar to the Sunyaev- photons because of annihilation at the boundary zones Zeldovich effect from the hot in clusters of galax- ies at relatively higher redshift z . Moreover, such for each antimatter cloud. Using Eq.(8), we can estimate ∼ rec the rate of the energy injection to the plasma as clouds would produce relatively higher but localized y- distortions on the CMB power spectrum, which corre- 2 dε dE ρclc sponds, in mean, to the COBE FIRAS limit but locally = ncl = (13) dt dt τev could be much higher. where ρcl = Mclncl and ncl is the spatial number den- sity of the ABC. Let us define the mass fraction of the ELECTROMAGNETIC CASCADES AND THE HYDROGEN RECOMBINATION ABC as fabc = ρcl/ρout which determines the energy release to the cosmic plasma at the epoch right before and during hydrogen recombination. Because of Comp- As in previous section, below we want to estimate pos- ton and bremsstrahlung interactions the energy density sible influence of the electromagnetic products of anni- of the products of annihilation leads to the CMB energy hilation on the balance at the epoch of the 4 hydrogen recombination. Using quantitative approach, for neutral and we can assume that because of the energy transfer for 2 2 513w the photons from E mpc down to E I = 13.6eV, σ 5.4α r ln (23) ∼ ∼ H ≃ f 0 825 + w  where I is the ionization potential, some fraction xe 1 could be reionized by the non-equilibrium quanta from≤ for the neutral hydrogen, where r2 = 3 σ and α is the the electromagnetic cascades in the plasma. The energy 0 8π T f Fermi constant. Note that for ionized hydrogen-helium balance for such ionization follows which contain 76% and 24% of corresponding mass frac-

Ix n ωε κ ∼ rec (18) tions of the light elements, the optical depth is close to e bar ≃ r |z z where ω is the efficiency of the energy transforms down 3 2 2 −1/2 3/2 to the ionization potential range and zrec 10 . ¿From Ω h Ω h 1+ z ≃ τ 2.3 b m , (24) Eq.(18) one obtains pc ≃ 0.022  0.125   1000  − − Ω h2 1+ z 1 κ 1 x ω 5.4 10−6 b e for wz 825 [18]. ≤ × 0.022  1000   2 10−4  0.1 Thus,≫ as one can see from Eq.(21)-(24), the energy loss ×   (19) for high-energy is determined by the inverse − Thus, the relatively small fraction ( 10 5) of the anni- Compton scattering off the CMB photons, whereas for ∼ hilation energy release can distort the kinetics of the cos- the high-energy photons the main process of the energy mological hydrogen recombination. The concrete mecha- loss is the electron-positron pair creation by neutral and 2 nism of the energy transition, starting from E mpc ionized . 1 GeV down to E I is connected with the electromag-≃ ∼ ∼ For the non-relativistic electrons (w < 1) the opti- netic cascades of the annihilation products with cosmic cal depth inverse Compton scattering is given by τIC 9 ≃ plasma. The annihilation of a nucleon and an antinucleon 2 10 τT , whereas for the photons it is close to the Thom- produces 5 pions, 3 of which are charged [15]. For × ∼ son optical depth. It has been shown [17, 18] that for charged pions, electromagnetic cascade appears due to high energy low energy photons conversion the spec- (+,−) (+,−) (−,+) (+,−) (+,−) → π µ +νµ decay including µ e tral number density is transition.→ The neutral pions decay into two→ photons 0 π 2γ. About 50% of the energy release is carried away dn(E) A −2 14 −1 → w + w (25) by the neutrino, about 30% by the photons and about dE ≃ σT nec  5  17% by electrons and positrons [16]. The spectrum of for E < E0, which corresponds to energy density the decay has a exponential shape n(E) exp( E/E0), where E E 70 MeV [15]. For the electron-positron∝ − 0 dn(E) 14Am cE 5 m c2 pair and ≥γ-quanta≃ the leading process of the energy re- ǫ = EdE e 0 1+ e . dE ≃ 5n σ  14  E  distribution down to ionization potential are Compton Z e T 0 (26) scattering by the CMB photons and the electron-positron Therefore, from Eq.(25)-(26) we can estimate the spectral pair production γ +(H,He) (H,He)+e+ +e−. When 2 → energy density at the range E I E mec , the Compton cross-section is well approxi- ≃ ≫ mated by the Klein-Nishina formula [17] 5 m c2 ǫ(E I) ln 2 ǫ e 1.7 10−3ǫ, (27) 2 3 mec 2E 1 ≃ ≃ 14 · E0 ≃ × σC σT ln 2 + , (20) ≃ 8  E  mec  2 which is much higher than the limit from Eq.(19). Note where σT is the Thomson cross-section. The corre- that an additional factor 0.47 results from the fraction of sponding optical depth for the Compton scattering is the annihilation energy related to electromagnetic com- − 2 −3 ponent. ω 8 10 4. As one can see, the non- τC 2.1σT mec /E0 7.5 10 τT , where ≃ ≃ × equilibrium ionization≃ × of the primordial hydrogen and  − Ω h2 Ω h2 1/2 1+ z 3/2 helium at the epoch of recombination is more effective σ = 56.7 b m (21) T 0.022  0.125   1000  than the distortions of the CMB blackbody power spec- tra. For the inverse Compton scattering of high energy elec- trons by the CMB photons the corresponding optical 2 9 Ωbh 3 DISTORTION OF THE RECOMBINATION depth is τIC 2 10 0.022 τC 1 for z 10 . ≃ ×   ≫ ≃ KINETICS The pair production cross-section σpc has the following 2 asymptotic for w = E/mec > 6 [18] The model of the hydrogen-helium recombination pro- 513w cess affected by the annihilation energy release can be σ 8.8α r2 ln (22) He ≃ f 0 825 + w  described phenomenologically in terms of the injection 5 of additional Lyα and Lyc photons [19, 20, 21]. For the anisotropy and polarization power spectrum, which we epochs of antimatter clouds evaporation (η 1 1) the will discuss in the following Section. We would like to − ≪ rate of ionized production nα and nc are defined point out that our assumption about the characteristic as time of the ABC evaporation, namely H(trec)τev 1 implies that at t t all the ABC disappear.∼ If dnα ≫ rec = εα(t) nb(t) H(t), H(t )τ 1, however, at the epoch of recombina- dt h i rec ev tion the corresponding≫ influence of the non-equilibrium dni = εi(t) nb(t) H(t), (28) photons can be characterized by the renormalization of dt h i the εα,i parameters in the following way: εα,i(z) = where H(t) and n (t) are the Hubble parameter and −1 h b i εα,i(zrec)(H(z)τev) where εα,i(zrec) corresponds to the the mean baryonic density, respectively, εα,i(t) are the models 1-3. The mean factor, which should necessarily efficiency of the Lyα and Lyc photon production. As one be taken into account, is the absorption of the high en- can see from Eq. (28) the dependence of εα,i(t) parame- ergy quanta from annihilation by the CMB photons. If, ters upon t (or z) allows us to model any kind for example, τev corresponds to the redshift zrei 100, of ionization regimes. For the ABC from Eq.(19)-(20) we then ∼ have 3/2 2 z m c − reion ε ω p [H(t)τ ] 1 f . (29) εα,i(zrec) εα,i(zrec) 0.03εα,i(zrec). (30) α,i ≃  I  ev abc ≃  zrec  ∼ If the time of evaporation is comparable with the Hubble For the relatively early reionization of the hydrogen by time H−1(t) at the epoch of recombination z z , then the products of annihilation, the ionization fraction of ∼ rec ε parameters are constant and proportional to f . matter xe = ne/ nb can be obtained from the balance α,i abc h i We demonstrate the effectiveness of our phenomeno- between the recombination and the ionization process logical approach in Fig. 1: the ionization fraction xe dx against redshift for the three models listed below: e = α (T ) n x2 + ε (z)(1 x )H(z)Θ(z z), dt − rec h bi e i − e ev − model 1: εα εi = 1; (31) • ≃ −13 4 −0.6 where αrec(T ) 4 10 T/10 K is the recom- model 2:εα εi = 10; ≃ × • ≃ bination coefficient ,zev corresponds to τev and T is the model 3: εα εi = 100. temperature of the plasma and nb = nb is the mean • ≃ value of the baryonic number densityh i of the matter. In The curves are produced from the modification of the an equilibrium between the recombination and the ioniza- recfast code [22]. For all models we use the fol- 2 tion process the ionization fraction of the matter follows lowing values of the cosmological parameters: Ωbh = 2 the well-known regime 0.022, Ωmh = 0.125, Ωλ = 0.7, h = 0.7, Ωm +Ωλ = 1, H(t)τev 1. x2(z) ε (z)H(z) ∼ e = i Θ(z z), (32) 1 x (z) α (z)n (z) ev − − e rec b 3 where H(z) = H0 Ωm(1 + z) +1 Ωm and nb −7 2 3 − ≃ 2 10 (Ωbh /0.02)(1p + z) . We would like to point out× that Eq.(32) can be used for any models of the late reionization, choosing the corresponding dependence of the εi(z) parameter on redshift. This point is vital in our modification of the recfast and the cmbfast packages, from which we can use the standard relation for matter temperature T (z) 270(1 + z/100)2 K and all the tem- perature peculiarities≃ of the reionization and clumping would be related with the εi(z) parameter through the mimicking of ionization history [23, 24]. From Eq.(32) one can find the maximal value of the ionization fraction at the moment z z ≃ ev FIG. 1: The ionization fractions for the model 1 (the solid 1 1 1/2 line), the model 2 (dash line) and model 3 (dash-dot line) as xmax = Γ+ 1+ Γ2 (33) a function of redshift. e −2  4 

As one can see from Fig. 1 all the models 1-3 pro- where Γ = ε (z )H(z )/[α (z )n (z )]. At 10 i ev ev rec ev b ev ≪ duce delays of recombination and can distort of the CMB z

CMB temperature proceeds faster than the ionized hy- we consider phenomenologically different variants of hy- drogen becoming neutral and for xe from Eq.(31) we get drogen reionization models by modifying the cmbfast code for the models 1-6 [25]. One addition problem ap- − t 1 pears if we are interested in observational constraints on max max the anti-matter fraction abundance related to the late xe(t) x 1+ x α(T )nbdt . (34) ≃ e e Z reionization of hydrogen at low redshift z < 20. After  τev  WMAP mission the most preferable value of the opti- cal depth of reionization is τ 0.17 [26], while it While the temperature of matter is close to the CMB reion ≃ temperature TCMB, the corresponding time of recombi- is also shown [24] that even the “standard model” with nation is zreion = 6 is not ruled out from the WMAP data (see also x [36]). Recently it has been argued that the late reion- ∆t e (xmax)−1t (T ), (35) rec e rec CMB ization could exist with two stages, one at zreion 15 ≃ dxe/dt ≃ ≃ | | and zreion 6 due to energy release from different pop- −1 −1 ≃ where trec = [α(T ) nb] τev,H (t). ulation of stars [28] or heavy neutrinos [29]. Without ≪ measurements with higher accuracy of the CMB polar- ization and temperature-polarization cross-correlation, it is unlikely to settle the issue on late reionization, even for WMAP resolution and sensitivity. However, any as- sumption about the optical depth of the late reionization are crucial for the estimation of any constraints on the ABC abundance. If, for example, we adopt the WMAP limit τreion 0.17 from the pure late reionization, the peak-like or≃ delayed recombination models from the ABC would by restricted very effective. But, if we assumes that roughly τ 0.04 comes from late reionization reion ∼ and τreion 0.06 0.12 is related to the ABC contam- ination at∼ relatively÷ high redshifts, then the constraints on the ABC abundance would be rather smaller than for the previous case. For estimation of the ABC features in the CMB anisotropy and polarization power spectrum FIG. 2: The ionization fractions for the model 4 (the solid line), the model 5(dash line) and model 6 (dash-dot line) as we use a more conservative limit on the optical depth of a function of redshift. reionization τreion 0.04 at zreion 6 in order to obtain the upper limit on∼ the ABC manifestation≃ in the CMB In addition to the models 1-3 we introduce the follow- data. ing three models: In Fig. 5 we plot the polarization power spectrum Cp(ℓ) model 4: ε ε =0.1 [(1 + z)/1000]3/2; • α ≃ i × for the model 1 -6 plus the standard single reionization 3/2 model at zreion 6 . The difference between model 1 and model 5: εα εi =1 [(1 + z)/1000] ; ≃ • ≃ × 2 mainly lies in the multipoles 2 <ℓ< 30. 3/2 model 6: εα εi = 10 [(1 + z)/1000] . • ≃ × As one can see from the Fig.4, in order of the magni- where zev = 200. In Fig.3 we plot the ionization fraction tude the εα,i parameters should be smaller than unity, −2 for the models 4-6 versus redshift. As one can see from if zev zrec and εα,i < 10 , if zev 200. So, using the Fig.3 the delay of recombination at z = 103 is smaller Eq.(29)≃ one can find that ≃ than in Fig.1, but the reionization appears at z z . ≃ ev At the range of redshifts z zev the behavior of ion- ization fraction follows Eq.(34)≫ with rapid decrease. The 3/2 properties of the models 4-6 are similar to those of the −1 I −5 1+ zev fabc = ω ε (H(t)τev) 2 1.7 10 , peak-like reionization model [24]. mpc ≤ ×  200  (36) while from the spectral distortion of the CMB blackbody THE CMB ANISOTROPY AND POLARIZATION power spectra we obtain FEATURES FROM THE MATTER-ANTIMATTER ANNIHILATION

2 In order to find out how sensitive is the polariza- y −4 Ωbh 1+ zev fabc 1.7 10 (37) tion power spectrum to the annihilation energy release, ≤ × 0.022  200  7

FIG. 5: The polarization power spectrum for the standard FIG. 3: The CMB power spectrum for the standard model model (the solid line), the model 4 (the dot line), the model without energy injection, (the solid line), the model 1(the 2 (the dash line) and the model 3 (the dash-dot line) as a dash line), model 2 (the dash-dot line) and model 3 (the lowest function of redshift. thick solid line) as a function of redshift. For ℓ< 500 we use the WMAP data [30], while for ℓ > 500 together with error bars the data is from CBI experiment [31].

FIG. 6: The TE cross-correlation power spectrum for the models listed in Fig.5 with the same notations.

FIG. 4: The CMB power spectrum for the standard model nations should be successfully removed and the accuracy without energy injection (the solid line), the model 4(dash of the Cℓ estimation would be close to the cosmic vari- line), 5 (dash-dot line) and 6 (the lowest thick solid line) as ance limit at low multipoles for both the temperature a function of redshift. The experimental data points are the , polarization and the TE cross-correlation same as in Fig.3. as well. The differences between the delayed recombination and early reionized universe models in comparison with the HOW PLANCK DATA CAN CONSTRAIN THE expected sensitivity of the Planck experiment can be ex- MASS FRACTION OF THE ANTIMATTER? pressed in terms of the power spectrum Ca,p(ℓ) (for the anisotropy, and the E component of polarization) [21] As is mentioned above, the observational constraint on a,p a,p the antimatter mass fraction fabc depends on the accu- 2 C (ℓ) C (ℓ) a,p i − j racy of the power spectrum estimation from the contem- Di,j (ℓ)=  a,p a,p , (38) Ci (ℓ)+ Cj (ℓ) porary and upcoming CMB data sets. As an example, how the upcoming Planck data would be important for where the indices i and j denote the different models , we would like to compare the upper limit on and a and p denote anisotropy and polarization. In or- the fabc parameter, using the WMAP and CBI data with der to clarify the manifestations of the complex ioniza- the expected sensitivity of the Planck data. We assume tion regimes in the models 1 and 4 we need to compare a,p that all the systematic effects and foreground contami- the peak to peak amplitudes of the Di,j (ℓ) function with 8

galactic or cluster scales, they could manifest themselves as point-like sources in the CMB map. For the upcoming Planck mission there are well defined predictions for the number density of bright point sources for each frequency band at the range 30 900 GHz. It would be interesting to obtain a new constraint÷ on the ABC fraction for large- scale clouds. This work is in progress. Acknowledgments: This paper was supported in part by Danmarks Grundforskningsfond through its support for the establishment of TAC.

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