Matter density perturbations in modified gravity models with arbitrary coupling between matter and geometry

TL;DR

This paper investigates matter density perturbations in modified gravity models with arbitrary matter-geometry coupling, deriving key parameters and applying a solvable toy model to connect theory with observational constraints.

Contribution

It derives the perturbation equations and effective gravitational parameters for these models, and analyzes a solvable toy model to link theoretical predictions with observational data.

Findings

Derived the perturbation equation for matter density

Obtained analytic solutions for the modified Friedmann equation

Constrained model parameters using astrophysical observations

Abstract

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 $\Sigma$ and $\eta$, 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.