1 + 3 covariant perturbations in power-law f(R) gravity

Abstract

We applied the 1+3 covariant approach around the Friedmann–Lemaître–Robertson–Walker (FLRW) background, together with the equivalence between f (R) gravity and scalar-tensor theory to study cosmological perturbations. We defined the gradient variables in the 1 + 3 covariant approach which we used to derive a set of evolution equations. Harmonic decomposition was applied to partial differential equations to obtain ordinary differential equations used to analyse the behavior of the perturbation quantities. We focused on dust dominated area and the perturbation equations were applied to background solution of αR +βRn model, n being a positive constant. The transformation of the perturbation equations into redshift dependence was done. After numerical solutions, it was found that the evolution of energy-density perturbations in a dust-dominated universe for different values of n decays with increasing redshift.