物质与几何任意耦合的修正引力模型中的物质密度扰动
Matter density perturbations in modified gravity models with arbitrary coupling between matter and geometry
摘要：
考虑了物质与引力任意耦合的理论，得到了视界下物质的微扰方程。此外，我们还导出了有效引力常量$G_{eff}$和两个参数$Σ$和$η$，它们与物质密度的微扰方程一起，对从增长因子和弱透镜观测中约束理论是有用的。最后，我们使用一个完全可解的玩具模型，表现出非平凡的现象学研究的理论的具体特点。我们得到了修正的Friedmann方程的比例因子$a$在时间$t$方面的解析解，并使用最古老的星团的年龄和原始核合成的界限，以约束我们的玩具模型的参数。
英文摘要：
We consider theories with an arbitrary coupling between matter and gravity and obtain the perturbation equation of matter on subhorizon scales. Also, we derive the effective gravitational constant $G_{eff}$ and two parameters $Σ$ and $η$, which along with the perturbation equation of the matter density are useful to constrain the theory from growth factor and weak lensing observations. Finally, we use a completely solvable toy model which exhibits nontrivial phenomenology to investigate specific features of the theory. We obtain the analytic solution of the modified Friedmann equation for the scale factor $a$ in terms of time $t$ and use the age of the oldest star clusters and the primordial nucleosynthesis bounds in order to constrain the parameters of our toy model.
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