Integrability conditions of quasi-Newtonian cosmologies in modified gravity

TL;DR

This paper explores the conditions under which certain shear-free cosmological models in modified gravity are mathematically consistent, extending previous relativistic results to f(R) dark energy models.

Contribution

It generalizes integrability conditions for shear-free perfect-fluid cosmologies to f(R) gravity, showing that anisotropic stress forms in these models satisfy the conditions.

Findings

Models with anisotropic fluid sources are generally inconsistent.

In f(R) gravity, integrability conditions are satisfied due to specific anisotropic stress forms.

Extended the quasi-Newtonian formulation to include f(R) dark energy models.

Abstract

We investigate the integrability conditions of a class of shear-free perfect-fluid cosmological models within the framework of anisotropic fluid sources, applying our results to f(R) dark energy models. Generalising earlier general relativistic results for time-like geodesics, we extend the potential and acceleration terms of the quasi-Newtonian formulation of integrable dust cosmological models about a linearized Friedmann-Lemaitre-Robertson-Walker background and derive the equations that describe their dynamical evolutions. We show that in general, models with an anisotropic fluid source are not consistent, but because of the particular form the anisotropic stress takes in f(R) gravity, the general integrability conditions, in this case, are satisfied.