Density Perturbation and Cosmological Evolution in the Presence of Magnetic Field in f R Gravity Models

Abstract

In this paper, we have investigated the density perturbations and cosmological evolution in the FLRW universe in the presence of a cosmic magnetic field, which may be assumed to mimic primordial magnetic fields. Such magnetic fields have sufficient strength to influence galaxy formation and cluster dynamics, thereby leaving an imprint on the CMB anisotropies. We have considered the FLRW universe as a representative of the isotropic cosmological model in the $1+3$ covariant formalism for $f\left(R\right)$ gravity. The propagation equations have been determined and analyzed, where we have assumed that the magnetic field is aligned uniformly along the $x$ -direction, resulting in a diagonal shear tensor. Subsequently, the density perturbation evolution equations have been studied, and the results have been interpreted. We have also indicated how these results change in the general relativistic case and briefly mentioned the expected change in higher-order gravity theories.