Covariant gauge-invariant perturbations in multifluid f(R) gravity

TL;DR

This paper develops a covariant gauge-invariant framework to analyze scalar perturbations in multifluid $f(R)$ gravity, providing new equations and solutions that reveal conditions for structure growth consistent with cosmological observations.

Contribution

It extends previous work by deriving a complete set of evolution equations for matter and curvature perturbations in multifluid $f(R)$ gravity, including exact solutions for specific regimes.

Findings

Growth rate of perturbations requires $n>2/3$ in $R^n$ gravity.

Provides exact solutions for perturbations on different scales.

Shows compatibility with the Mészáros effect for certain $f(R)$ models.

Abstract

We study the evolution of scalar cosmological perturbations in the (1+3)- covariant gauge-invariant formalism for generic $f(R)$ theories of gravity. Extending previous works, we give a complete set of equations describing the evolution of matter and curvature fluctuations for a multi-fluid cosmological medium. We then specialize to a radiation-dust fluid described by barotropic equations of state and solve the perturbation equations around a background solution of $R^{n}$ gravity. In particular we study exact solutions for scales much smaller and much larger than the Hubble radius and show that $n>2/3$ in order to have a growth rate compatible with the M\'esz\'aros effect.