Integrability conditions of quasi-Newtonian cosmologies in modified gravity

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. Generalizing earlier general relativistic results for timelike geodesics, we extend the potential and acceleration terms of the quasi-Newtonian formulation of integrable dust cosmological models about a linearized Friedmann-Lemaître-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 πab takes in f(R) gravity, the general integrability conditions in this case are satisfied.