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arXiv 2103.10639astro-ph.COgr-qc
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二次效应对CMB B模偏振的统一处理

Unified approach to secondary effects on the CMB B-mode polarization

Toshiya Namikawa, Atsushi Naruko, Ryo Saito, Atsushi Taruya, Daisuke Yamauchi

摘要:

本文发展了一种系统的、统一的方法来估计宇宙微波背景(CMB)极化的所有可能的二次(即非原生)非线性效应,称为视程曲线积分方法。在这种方法中,极化光子的玻尔兹曼方程被重写为沿着受扰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。该方法解决了在光子自由流场中求解具有非线性引力效应的Boltzmann方程组的困难,从而将CMB透镜的标准重映方法统一为求解具有非线性碰撞效应的Boltzmann方程的直接方法。在本文中,我们推导公式:(i)包括所有的非线性效应;(ii)可以处理扩展的源,如再电离后的贡献。它提供了一个坚实的框架,讨论可能的系统在标准估计的CMB透镜的重映射方法。作为一个明确的演示,我们估计的次级B模功率谱引起的所有前景引力效应:透镜,红移,时间延迟,发射角,和偏振旋转效应。我们正确地定义这些效应,使它们没有任何重叠,也没有忽略任何效应。然后,我们表明,这些影响只给出了0.001-0.01%的数量级的校正标准透镜诱导的B-模式功率谱的和谐$Λ$冷暗物质模型。我们的结果证实了在即将到来的CMB实验中使用重映射方法的可靠性,该实验旨在探测张量标量比为$r \sim 10^{-3}$的原始引力波。

英文摘要:

We develop a systematic and unified approach to estimate all possible secondary (i.e. 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 $r \sim 10^{-3}$.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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