小红移和中等红移时引力扩展理论的运动学重建
Kinematic reconstructions of extended theories of gravity at small and intermediate redshifts
摘要：
在过去的几十年里，广义相对论的扩展一直受到更多的关注，特别是考虑到标准$Λ$ CDM范式在中高红移区域可能出现的故障。如果广义相对论不是引力的终极理论，那么在均匀和各向同性的宇宙中修改爱因斯坦的引力可能是描述当前宇宙加速度的可行途径。在这里，我们把注意力集中在两类扩展理论上，即$f(R)$和$f(R,G)$ -引力。我们参数化的哈勃函数的有效正压流体的装置，通过校准我们的曲线的形状，通过一些最合适的暗能量参数化，XCDM，CPL，WP。然后，利用Ricci标量和Gauss-Bonnet拓扑不变量与红移$z$的对应关系，用相应的$f(z)$辅助函数改写了$f(R,G)$.该方案使人们能够得到数值形状的$f(R,G)$和$f(R)$模型，通过一个粗粒度的逆散射过程。虽然我们的方法与广义相对论的最简单的扩展相一致，但它留下了一种可能性，即$f(R)$和$f(R,G)$的最合适的形式是一阶有理Padé多项式。这些近似似乎是兼容的中间红移域内的数值重建和匹配相当不错的小红移测试。
英文摘要：
In the last few decades, extensions of General Relativity have reached always more attention especially in view of possible breakdowns of the standard $Λ$CDM paradigm at intermediate and high redshift regimes. If General Relativity would not be the ultimate theory of gravity, modifying Einstein's gravity in the homogeneous and isotropic universe may likely represent a viable path toward the description of current universe acceleration. We here focus our attention on two classes of extended theories, i.e. the $f(R)$ and $f(R,G)$-gravity. We parameterize the so-obtained Hubble function by means of effective barotropic fluids, by calibrating the shapes of our curves through some of the most suitable dark energy parameterizations, XCDM, CPL, WP. Afterwards, by virtue of the correspondence between the Ricci scalar and the Gauss-Bonnet topological invariant with the redshift $z$, we rewrite $f(R,G)$ in terms of corresponding $f(z)$ auxiliary functions. This scheme enables one to get numerical shapes for $f(R,G)$ and $f(R)$ models, through a coarse-grained inverse scattering procedure. Although our procedure agrees with the simplest extensions of general relativity, it leaves open the possibility that the most suitable forms of $f(R)$ and $f(R,G)$ are rational Padé polynomials of first orders. These approximations seem to be compatible with numerical reconstructions within intermediate redshift domains and match fairly well small redshift tests.
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。
