Linear perturbations of an anisotropic Bianchi I model with a uniform magnetic field

TL;DR

This paper investigates how a uniform magnetic field influences the growth of cosmological perturbations in an anisotropic Bianchi I universe, providing a refined relativistic treatment that includes anisotropic effects.

Contribution

It develops a consistent relativistic framework for perturbations in a Bianchi I universe with a magnetic field, extending previous isotropic models to include anisotropic effects.

Findings

Refined relativistic solutions for perturbations with magnetic fields.

Recovery of known Newtonian results in the appropriate limit.

Inclusion of anisotropic effects within the relativistic perturbation theory.

Abstract

In this work, we study the effect of a magnetic field on the growth of cosmological perturbations. We develop a mathematical consistent treatment in which a perfect fluid and a uniform magnetic field evolve together in a Bianchi I universe. We then study the energy density perturbations on this background with particular emphasis on the effect of the background magnetic field. We develop a full relativistic solution which refines previous analysis in the relativistic limit, recovers the known ones in the Newtonian treatment with adiabatic sound speed, and it adds anisotropic effects to the relativistic ones for perturbations with wavelength within the Hubble horizon. This represents a refined approach on the perturbation theory of an isotropic universe in GR, since most of the present studies deal with fully isotropic systems.