The Accelerated Recombination, and the ACBAR and WMAP data
aa r X i v : . [ a s t r o - ph ] A p r Submitted to the Astrophysical Journal Letter
Preprint typeset using L A TEX style emulateapj v. 08/22/09
ACCELERATED RECOMBINATION, AND THE ACBAR AND WMAP DATA
Jaiseung Kim and Pavel Naselsky
Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen, Denmark
Submitted to the Astrophysical Journal Letter
ABSTRACTWe have investigated deviation from the standard recombination process, using the ACBAR 2008and the WMAP 3 year data. In this investigation, we have considered the possibility of acceleratedrecombination as well as delayed recombination. We find that accelerated recombination is as likelyas delayed recombination, and there is some degeneracy between ǫ α and { n s , log[10 A s ], H } . Subject headings: cosmology: cosmic microwave background – methods: data analysis INTRODUCTION
The ionization history of the cosmic plasma is oneof the most important part of the modern cosmol-ogy. Based on well-known atomic physics princi-ples, the theory of recombination of the cosmologi-cal hydrogen provides remarkable information aboutthe most fundamental properties of the matter inthe Universe through the anisotropy and polariza-tion of the Cosmic Microwave Background (CMB). Inthis Letter, we discuss different modification of thismodel and some of the observational consequences ofthe nonstandard models of recombination, proposedin Peebles et al. (2001); Naselsky and Novikov (2002);Doroshkevich et al. (2003); Sommer-Larsen et al. (2004)(see also Bean et al. (2007) and the references therein).The early source of Ly- α photons may lead to thedeviations from the standard recombination process,hence affecting the CMB anisotropy (Peebles et al. 2001;Doroshkevich et al. 2003).The major distortions of the theoretically predictedpower spectrum, which are related to acceleration ordelay of the hydrogen recombination at the redshift z rec ≃ z = z rec . This is why the futurePLANCK polarization data will provide a unique oppor-tunity to test the nonstandard models of the recombina-tion with unprecedented accuracy. However, even usingthe recently available ACBAR 2008 data and WMAP 3year data, we can get very informative restrictions on theparameters of the distortion models. In this Letter, weuse the latest high resolution ACBAR data in combina-tion with the WMAP data. The importance of the highresolution data seems to be quite obvious, since the ma-jor distortion on the CMB anisotropy power spectrum isrelated to the spatial scales on the order of ∆ ∼
10 Mpc,which is ∼ −
5% of the width of the last scatteringsurface. In addition to the models of delayed recombi-nation (Bean et al. 2007), in this Letter, we consider themodels of accelerated recombination, trying to constrainthe cosmological model, based on the WMAP and theACBAR data. We show that the WMAP data or thecombination of the WMAP and the ACBAR data reveal
Electronic address: [email protected] some tendency in favor of the “accelerated” recombina-tion, while the constraint by the ACBAR data alone ismore or less neutral. THE DEVIATION FROM THE STANDARDRECOMBINATION PROCESS
The production rate of extra resonance photons n α isassumed to be (Peebles et al. 2001; Doroshkevich et al.2003): d n α d t = ǫ α ( z ) H ( z ) n, where n is the number density of atoms, H ( z ) is theHubble expansion rate at a redshift z , and ǫ α ( z ) is a pa-rameter dependent on the production mechanism. Sincethe width of the recombination is very small in com-parison to the horizon of the last scattering surface L ls ,the dependence of ǫ α ( z ) on z can be parametrized as ǫ α ( z rec ) + o (∆ /L ls ) . A simple parametrization usinga constant effective value for ǫ α ( z rec ) ≡ ǫ α with theWMAP data shows that ǫ α < .
32 (Bean et al. 2007).Here ǫ α of negative values and positive values corre-sponds to accelerated recombination and delayed recom-bination respectively. The delayed recombination maybe caused by the existence of the source for extra res-onance photons (Peebles et al. 2001; Doroshkevich et al.2003; Bean et al. 2007) and accelerated recombinationmay occur when there is clustering of baryonic mat-ter on small scales (Naselsky and Novikov 2002). Thepossibility of accelerated recombination has not beengiven proper consideration, while the possibility of de-layed acceleration has been investigated by many authorsincluding (Peebles et al. 2001; Doroshkevich et al. 2003;Bean et al. 2007).In this Letter, we have investigated the possibilityof accelerated recombination as well, using the recentACBAR 2008 data (Reichardt et al.) and WMAP 3 yeardata (Hinshaw and et al. 2007). Through small modifi-cations to the widely used RECFAST code and the
CosmoMC package (Lewis and Bridle 2002), we have included theparameter ǫ α in the cosmological parameter estimation,where we have explored the seven parameter space (sixcosmological parameters + ǫ α ). We have assumed aconstant effective value for ǫ α with the uniform prior − . ≤ ǫ α ≤ .
3, based on (Doroshkevich et al. 2003;Bean et al. 2007). It should be noted that we have in-cluded ǫ α of negative values in the range − . ≤ ǫ α <
0, Jaiseung Kim and Pavel Naselskywhile the investigation by (Bean et al. 2007) did not in-clude ǫ α of any negative values for the prior. The param-eter space exploration was made through fitting the CMBpower spectra of a flat ΛCDM model to the TT powerof the ACBAR, and the TT, TE and EE power of theWMAP data. The marginalized distribution shows theprobability in the reduced dimension of parameter space,and the mean likelihood shows how good a fit can be ex-pected (Lewis and Bridle 2002). In the Fig. 1, we showsthe marginalized distribution and mean likelihoods of ǫ α ,given the ACBAR and the WMAP data. As shown in −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.0800.20.40.60.81 ε α WMAP+ACBARWMAP ACBAR−0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.080.20.40.60.81 ε α WMAP+ACBARWMAP ACBAR
Fig. 1.— the marginalized distribution (top), the mean likelihood(bottom). The normalization is chosen such that the peak value isequal to unity.
Fig. 1, ǫ α of negative values is as likely as that of positivevalues, implying the possibility of accelerated recombina-tion. When constrained by the WMAP data alone or byboth of the WMAP and the ACBAR, ǫ α of negative val-ues is more likely than that of positive values, althoughthis is not in the constraint by the ACBAR data alone.This discrepancy in the constraint by the ACBAR alonemay be attributed to the propagation of the uncertaintyof other degenerate cosmological parameters to ǫ α . Thedegeneracy between other cosmological parameters and ǫ α may be noticed in Fig. 2 and 3, where we have plot-ted 1- σ and 2- σ contours of the marginalized distributionand mean likelihoods in the plane of ǫ α vs Ω b h , Ω c h , τ , n s , log[10 A s ], H . We find that there exists somedegeneracy between ǫ α and { n s , log[10 A s ], H } . Fromthe Fig. 2 and 3, we find again that ǫ α of negative valuesis more likely than that of positive values, when con-strained by the WMAP alone or by both of the WMAPand the ACBAR. ε α Ω b h −0.06 −0.02 0.020.0220.024 ε α −0.06 −0.02 0.020.020.0220.024 ε α −0.05 0 0.050.0150.020.025 ε α Ω c h −0.06 −0.02 0.020.10.110.12 ε α −0.06 −0.02 0.020.10.12 ε α −0.05 0 0.050.10.150.2 ε α τ −0.06 −0.02 0.020.050.10.15 ε α −0.06 −0.02 0.020.050.10.15 ε α −0.05 0 0.050.20.40.6 ε α n s −0.06 −0.02 0.020.90.951 ε α −0.06 −0.02 0.020.90.951 ε α −0.05 0 0.050.811.2 ε α l og [ A s ] −0.06 −0.02 0.0233.2 ε α −0.06 −0.02 0.022.833.2 ε α −0.05 0 0.0533.54 ε α H −0.06 −0.02 0.02050100 ε α −0.06 −0.02 0.02050100 ε α −0.05 0 0.05050100 Fig. 2.—
The marginalized distribution on ǫ α vs 6 basic param-eters, using the WMAP + ACBAR (left), the WMAP (middle),and the ACBAR (right). The distortion on the CMB black body spectrum bythe nonstandard recombination process ( | ǫ α | <
1) ispractically negligible in comparison with the distortionby the re-ionization history (see Naselsky and Chiang(2004) for details), and is consistent with the COBE FI-RAS data constraint (Fixsen et al. 1996). CONCLUSION AND SUMMARY
We have investigated the distortion on the standardrecombination process, using the ACBAR 2008 data andthe WMAP 3 year data. We find that the constraint byccelerated Recombination 3 ε α Ω b h −0.06 −0.02 0.020.0220.024 ε α −0.06 −0.02 0.020.020.0220.024 ε α −0.05 0 0.050.0150.020.025 ε α Ω c h −0.06 −0.02 0.020.10.110.12 ε α −0.06 −0.02 0.020.10.12 ε α −0.05 0 0.050.10.150.2 ε α τ −0.06 −0.02 0.020.050.10.15 ε α −0.06 −0.02 0.020.050.10.15 ε α −0.05 0 0.050.20.40.6 ε α n s −0.06 −0.02 0.020.90.951 ε α −0.06 −0.02 0.020.90.951 ε α −0.05 0 0.050.811.2 ε α l og [ A s ] −0.06 −0.02 0.0233.2 ε α −0.06 −0.02 0.022.833.2 ε α −0.05 0 0.0533.54 ε α H −0.06 −0.02 0.02050100 ε α −0.06 −0.02 0.02050100 ε α −0.05 0 0.05050100 Fig. 3.—
The mean likelihoods of ǫ α vs 6 basic parameters, us-ing the WMAP + ACBAR (left), the WMAP (middle), and theACBAR (right). the ACBAR and the WMAP data favors the possibilityof accelerated recombination. As seen in Fig. 2 and3, there exists some level of degeneracy between ǫ α and other cosmological parameters. Partially due tothese degeneracies, the constraint by the WMAP andthe ACBAR are not powerfull enough to rule out thepossibility of delayed recombination or the standardrecombination at 1- σ confidence level. The polar-ization anisotropy is quite sensitive to the distortion(Doroshkevich et al. 2003). Hence we will be able toimpose tighter constraints on the distortion models,when the temperature and polarization data from theupcoming Planck satellite become available.We are grateful to Antony Lewis for his guidance on themodification of the CosmoMC package. We also thank theanonymous referee for helpful suggestion, which leads tothe improvement of this paper. We acknowledge the useof the Legacy Archive for Microwave Background DataAnalysis (LAMBDA) and ACBAR 2008 data. Our nu-merical analysis was performed on the supercomputingfacility of the Danish Center for Scientific Computing.This work was supported by FNU grants 272-06-0417,272-07-0528 and 21-04-0355.
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