【摘要】 在宇宙早期的退耦过程中,光子与电子发生Thompson散射.光子气体空间分 布的各向异性通过Thompson散射而产生宇宙微波背景辐射的极化,并为最近WMAP观 测到.从光子气体的Boltzmann方程出发,采用一般的光深函数,分别积分给出原初密度 扰动和残余引力波产生的微波背景辐射极化的近似解析解,结果适用于一般的复合过程. 密度扰动FS所产生极化的近似解析解为βS≈-CFS(τd)△τd,其τd和△τd分别为退 耦时刻和退耦宽度,系数C≈(0.08-0.12),明显依赖于复合模型.残余引力波扰动FT 产生极化的积分稍微复杂,在长波近似下我们对原初扰动按波数进行幂级数展开,保留到 两项FT≈FT(1)＋FT(2),分别积分,给出近似解析解βT≈-[CFT(1)(τd)+DFT(2)(τd)]△τd. 第一项的极化与密度扰动类似,结论也相同;但第二项的系数D≈(0.22-0.32),远大于 系数C.我们的近似解析解有助于理解背景辐射的温度-极化交叉关联和检测残余引力 波对背景辐射各向异性的贡献.更多还原

【Abstract】 During the decoupling process in the early Universe, photons were interacting with electrons by Thompson scattering. The anisotropies 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 Cosmic Microwave Backgroud (CMB) radiation 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 polarizations 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 βS ≈ -CFs(τd)Δτd, where τd and Δτd are the decoupling time and the decoupling duration, respectively, and C ≈ (0.08 - 0.12) depending on recombination models. For the tensorial 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 polarizations, βT ≈ -[CFT(1)(τd) + DFT(τd)]Δτd, 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 anisotropies of CMB.更多还原