Mathematics – Logic
Scientific paper
Jan 2005
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005acasn..46....1z&link_type=abstract
Acta Astronomica Sinica, vol. 46, no. 1, p. 1-17
Mathematics
Logic
3
Cosmic Microwave Background, Early Universe, Cosmological Parameters
Scientific paper
During the decoupling process in the early Universe, photons were interacting with electrons by Thompson scattering. The anisotropy in the spatial distribution of photon gas will give rise to a net polarization of photon gas after this scattering. This is the origin of the polarization of the Comic Microwave Background Radiation (CMB) that has just been observed recently. There has been a simple approximate analytic solution of polarization consisting of the primordial perturbation at the peak of the decoupling, multiplying the decoupling duration. In this paper, starting from the Boltzmann equation for the photons, we calculate analytically the CMB polarization caused by the scalar and tensor types of the primordial perturbations for a general expression for the optical depth function, and the results are valid for a generic recombination process. For the scalar type of perturbations FS, the resulting approximate analytical polarization is ?S?- C FS(?d)??d, where ?d and ??d are the decoupling time and the decoupling duration, respectively, and C ?(0.08~0.12) depending on recombination models. For the tensor type of perturbations, the calculation is a bit more complicated, and we do it in the long wave-length limit. By expanding the perturbation function in terms of the wave number and keeping the first two terms FT ? FT(1) + FT(2), we integrate and obtain the analytic expressions for the polarization,
?T?- [C FT(1) (?d) + D FT(2) (?d)] ??d, where D ? (0.22 ~0.32) , also depending on recombination models.
Our results may help to interpret the observed temperature-polarization cross correlation, and to disentangle the contribution by relic gravitational waves from that by density perturbations to the polarization and temperature anisotropy of CMB.
Hao He
Zhang Yajing
Zhao Wenbing
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