非均匀宇宙学中光传播的孤立非线性
Isolating non-linearities of light propagation in inhomogeneous cosmologies
摘要：
本文利用双定域测地线算子，给出了几何光学中光传播的一个新公式。我们开发了BiGONLight Mathematica软件包，该软件包专门设计用于应用此框架计算数值相对论中的光学可观测量。我们的软件包可用于光传播的尺度和红移范围很广，并接受时空度规的数值和分析输入。在本文中，我们专注于两个宇宙学观测，红移和角直径的距离，专门分析后牛顿近似内建模的壁宇宙。通过这种选择和分析形式的输入度量，我们能够通过比较和隔离来自牛顿和后牛顿近似的贡献来估计光传播的非线性，而不是线性微扰理论。我们还澄清的作用，占主导地位的后牛顿的贡献所代表的线性初始种子，严格地说，是缺席的牛顿治疗。我们发现，后牛顿非线性校正低于$1\%$，与文献中以前的结果一致。
英文摘要：
A new formulation for light propagation in geometric optics by means of the Bi-local Geodesic Operators is considered. We develop the BiGONLight Mathematica package, uniquely designed to apply this framework to compute optical observables in Numerical Relativity. Our package can be used for light propagation on a wide range of scales and redshifts and accepts numerical as well as analytical input for the spacetime metric. In this paper we focus on two cosmological observables, the redshift and the angular diameter distance, specializing our analysis to a wall universe modeled within the post-Newtonian approximation. With this choice and the input metric in analytical form, we are able to estimate non-linearities of light propagation by comparing and isolating the contributions coming from Newtonian and post-Newtonian approximations as opposed to linear perturbation theory. We also clarify the role of the dominant post-Newtonian contribution represented by the linear initial seed which, strictly speaking, is absent in the Newtonian treatment. We found that post-Newtonian non-linear corrections are below $1\%$, in agreement with previous results in the literature.
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