残余引力波产生的电离CMB各向异性和极化的近似解析谱
Approximate Analytic Spectra of Reionized CMB Anisotropies and Polarization generated by Relic Gravitational Waves
摘要：
本文给出了由残余引力波（RGW）产生的宇宙微波背景辐射（CMB）各向异性和极化的再电离谱$C_l^{XX}$的近似解析计算。探讨了三种简单的再电离模型，其可见度函数用高斯型函数近似拟合。我们推导出了解析的极化$β_l$和温度各向异性$α_l$，两者都由两个与RGW成比例的项组成，在去耦和再电离时也是如此。证明了$β_l$和$α_l$与再电离时间$η_r$、持续时间$Δη_r$和光学深度$κ_r$的显着依赖性。此外，$β_l$和$α_l$中含有不同系数的$κ_r$，极化谱$C_l^{EE}$是$C_l^{BB}$比$C_l^{TT}$更灵敏的再电离探针.这些结果有助于检查的再电离效应，特别是，$κ_r$与归一化振幅和RGWs的初始光谱指数的简并。还发现，再电离也会导致$C_l^{TE}$的零多极$l_0$的$κ_r$依赖性移位$Δl\sim 20$，为了检测RGW的痕迹，应该包括这种效应。与数值计算结果相比，解析$C_l^{XX}$作为近似方法存在一定的局限性.对于$l\simeq (30, 600)$范围内的主峰，三种模型的误差均为$\le 3%$。在再电离凸块的$l < 20$范围内，两个扩展再电离模型中的$C_l^{EE}$和$C_l^{BB}$的误差为$\le 15%$，而$C_l^{TT}$和$C_l^{TE}$对$l<10$的偏离要大得多。突然再电离模型中的颠簸太低了。
英文摘要：
We present an approximate, analytical calculation of the reionized spectra $C_l^{XX}$ of cosmic microwave background radiation (CMB) anisotropies and polarizations generated by relic gravitational waves (RGWs). Three simple models of reionization are explored, whose visibility functions are fitted by gaussian type of functions as approximations. We have derived the analytical polarization $β_l$ and temperature anisotropies $α_l$, both consisting of two terms proportional to RGWs at the decoupling and at the reionization as well. The explicit dependence of $β_l$ and $α_l$ upon the reionization time $η_r$, the duration $Δη_r$, and the optical depth $κ_r$ are demonstrated. Moreover, $β_l$ and $α_l$ contain $κ_r$ in different coefficients, and the polarization spectra $C_l^{EE}$ are $C_l^{BB}$ are more sensitive probes of reionization than $C_l^{TT}$. These results facilitate examination of the reionization effects, in particular, the degeneracies of $κ_r$ with the normalization amplitude and with the initial spectral index of RGWs. It is also found that reionization also causes a $κ_r$-dependent shift $Δl\sim 20$ of the zero multipole $l_0$ of $C_l^{TE}$, an effect that should be included in order to detect the traces of RGWs. Compared with numerical results, the analytical $C_l^{XX}$ as approximation have the limitation. For the primary peaks in the range $l\simeq (30, 600)$, the error is $\le 3%$ in three models. In the range $l < 20$ for the reionization bumps, the error is $\le 15%$ for $C_l^{EE}$ and $C_l^{BB}$ in the two extended reionization models, and $C_l^{TT}$ and $C_l^{TE}$ have much larger departures for $l<10$. The bumps in the sudden reionization model are too low.
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