Unified approach to secondary effects on the CMB B-mode polarization
Unified approach to secondary effects on the CMB B-mode polarization
复制标题
CMB B 模式偏振二次效应的统一方法
DOI：
10.1088/1475-7516/2021/10/029
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发表时间：
2021
影响因子：
6.4
通讯作者：
Yamauchi Daisuke
中科院分区：
文献类型：
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作者：
Namikawa Toshiya;Naruko Atsushi;Saito Ryo;Taruya Atsushi;Yamauchi Daisuke
我们发展了一种系统和统一的方法来估计宇宙微波背景(CMB)偏振的所有可能的次要(即非原始)非线性效应，称为视线积分方法。在这种方法中，偏振光子的Boltzmann方程被重写为沿扰动宇宙中的精确测地线的视线积分，而不是线性阶CMB计算中使用的背景宇宙中的测地线。这种方法解决了在光子自由流区求解具有非线性引力效应的Boltzmann方程的困难，从而将CMB透镜的标准重映射方法统一为求解非线性碰撞效应的Boltzmann方程的直接方法。在本文中，我们推导出公式：(I)包括所有的非线性效应；(Ii)可以处理扩展的源，如重新电离后的贡献。它提供了一个坚实的框架，以讨论可能的系统论的标准估计的CMB透镜的重新映射方法。作为一个明确的例子，我们估计了所有前景引力效应：透镜效应、红移效应、时延效应、发射角效应和偏振旋转效应所引起的次级B模功率谱。我们恰当地定义了这些影响，这样它们就不会有任何重叠，也不会忽视任何影响。然后，我们证明了这些效应对协调Λ冷暗物质模型中标准透镜诱导的B模功率谱只有0.001-0.01%量级的修正。我们的结果证实了在即将到来的CMB实验中使用重新映射方法的可靠性，该实验旨在探测张量与标量比为r∼10-3的原始引力波。
We develop a systematic and unified approach to estimate all possible secondary (ie non-primordial) nonlinear effects to the cosmic microwave background (CMB) polarization, named curve-of-sight integration approach. In this approach, the Boltzmann equation for polarized photons is rewritten in a line-of-sight integral along an exact geodesic in the perturbed universe, rather than a geodesic in the background universe used in the linear-order CMB calculation. This approach resolves the difficulty to solve the Boltzmann hierarchy with the nonlinear gravitational effects in the photon free-streaming regime and thus unifies the standard remapping approach for CMB lensing into the direct approach solving the Boltzmann equation for the nonlinear collisional effects. In this paper, we derive formulae that:(i) include all the nonlinear effects;(ii) can treat extended sources such as the contributions after the reionization. It offers a solid framework to discuss possible systematics in the standard estimation of CMB lensing by the remapping approach. As an explicit demonstration, we estimate the secondary B-mode power spectrum induced by all foreground gravitational effects: lensing, redshift, time-delay, emission-angle, and polarization-rotation effects. We define these effects properly so that they do not have any overlap, also without overlooking any effect. Then, we show that these effects only give corrections of the order of 0.001-0.01% to the standard lensing-induced B-mode power spectrum in the concordance Λ cold dark matter model. Our result confirms the reliability of using the remapping approach in upcoming CMB experiments aiming to detect the primordial gravitational waves with the tensor-to-scalar ratio of r∼ 10-3.