膜致重力中的大尺度结构I。微扰理论
Large-Scale Structure in Brane-Induced Gravity I. Perturbation Theory
摘要：
本文用微扰理论研究了膜致引力中视界下微扰的增长。我们解决的线性演化的扰动利用规范变换下的对称性沿额外的维度解耦的体方程的准静态近似，我们认为这可能是一个更好的近似在大尺度比以前认为。然后，我们研究的非线性体和膜方程，集中在运作的Vainshtein机制，该理论成为广义相对论（GR）在小尺度。我们表明，在功率谱的水平上，一个很好的近似，在修改后的重力部门的非线性的影响可能会被吸收到一个重整化的引力常量。由于透镜势和密度扰动之间的关系完全不受这些理论中额外物理的影响，在这种近似下，修正的引力可以用一个函数来描述，一个依赖于空间和时间的非相对论运动的有效引力常量。我们开发了一个重新计算方案来计算它，并提供预测的非线性功率谱。在大规模的双谱的水平上，领先的顺序校正获得的标准微扰理论技术，并显示，抑制的膜弯曲模式导致的特征签名在重力产生的非高斯，通用的模型，成为GR在小尺度上通过二阶导数相互作用。我们在这项工作中的预测进行比较的数值模拟在一个配套文件。
英文摘要：
We study the growth of subhorizon perturbations in brane-induced gravity using perturbation theory. We solve for the linear evolution of perturbations taking advantage of the symmetry under gauge transformations along the extra-dimension to decouple the bulk equations in the quasistatic approximation, which we argue may be a better approximation at large scales than thought before. We then study the nonlinearities in the bulk and brane equations, concentrating on the workings of the Vainshtein mechanism by which the theory becomes general relativity (GR) at small scales. We show that at the level of the power spectrum, to a good approximation, the effect of nonlinearities in the modified gravity sector may be absorbed into a renormalization of the gravitational constant. Since the relation between the lensing potential and density perturbations is entirely unaffected by the extra physics in these theories, the modified gravity can be described in this approximation by a single function, an effective gravitational constant for nonrelativistic motion that depends on space and time. We develop a resummation scheme to calculate it, and provide predictions for the nonlinear power spectrum. At the level of the large-scale bispectrum, the leading order corrections are obtained by standard perturbation theory techniques, and show that the suppression of the brane-bending mode leads to characteristic signatures in the non-Gaussianity generated by gravity, generic to models that become GR at small scales through second-derivative interactions. We compare the predictions in this work to numerical simulations in a companion paper.
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