标题： 在$Λ$冷暗物质模型和$f(R)$修改引力理论中非均匀扰动的演化 显示英文标题

标题： On the evolution of inhomogeneous perturbations in the $Λ$CDM model and $f(R)$ modified gravity theories

摘要： 我们关注低红移处的弱非均匀宇宙模型，这些模型由Lemaître-Tolman-Bondi（LTB）度规描述。 本工作的主要目的是比较在$\Lambda$冷暗物质（CDM）宇宙学模型和$f(R)$修改引力理论中非均匀扰动的演化情况，同时考虑平坦的弗里德曼-勒梅特-罗伯逊-沃克（FLRW）度规作为背景。 更具体地说，我们采用乔丹框架中的等效标量-张量形式，在该形式中，$f(R)$函数的额外自由度被转化为非最小耦合的标量场。 我们分别按照时间与空间来研究局部非均匀性的演化，采用线性扰动方法。 然后，我们在两种宇宙学模型中获得了球对称解。 我们的结果使我们能够区分宇宙学常数和修改引力情景的存在，因为在乔丹框架中会出现一种特殊的类似尤卡夫的径向扰动解。 此外，扰动的径向分布不依赖于$f(R)$函数的具体选择，因此我们的结果适用于任何$f(R)$模型。 显示英文摘要

摘要： We focus on weak inhomogeneous models of the Universe at low redshifts, described by the Lema\^itre-Tolman-Bondi (LTB) metric. The principal aim of this work is to compare the evolution of inhomogeneous perturbations in the $\Lambda$CDM cosmological model and $f(R)$ modified gravity theories, considering a flat Friedmann-Lema\^itre-Robertson-Walker (FLRW) metric for the background. More specifically, we adopt the equivalent scalar-tensor formalism in the Jordan frame, in which the extra degree of freedom of the $f(R)$ function is converted into a non-minimally coupled scalar field. We investigate the evolution of local inhomogeneities in time and space separately, following a linear perturbation approach. Then, we obtain spherically symmetric solutions in both cosmological models. Our results allow us to distinguish between the presence of a cosmological constant and modified gravity scenarios, since a peculiar Yukawa-like solution for radial perturbations occurs in the Jordan frame. Furthermore, the radial profile of perturbations does not depend on a particular choice of the $f(R)$ function, hence our results are valid for any $f(R)$ model.