# Cosmological dynamics of magnetic Bianchi I in viable $f(R)$ models of gravity

## TL;DR

This paper analyzes the cosmological dynamics of magnetic fields in Bianchi I universes within viable $f(R)$ gravity models, revealing an initial anisotropic phase influenced by primordial magnetic fields, differing from standard isotropic models.

## Contribution

It introduces a dynamical system analysis of magnetic Bianchi I models in $f(R)$ gravity, uncovering an additional anisotropic fixed point and the role of primordial magnetic fields in shear evolution.

## Key findings

- Discovery of an additional anisotropic fixed point before the matter epoch.
- Primordial magnetic fields influence shear evolution, scaling as $\sigma o t^{-1/3}$.
- Universe transitions from initial isotropy to anisotropic intermediate, then to late-time acceleration.

## Abstract

Standard dynamical system analysis of Einstein-Maxwell equation in $f(R)$ theories is considered in this work. We investigate cosmological dynamics of a uniform magnetic field in the Orthogonal Spatially Homogeneous (OSH) Bianchi type I universe with viable $f(R)$ models of gravity. In this work, the $f(R) = R -\alpha R^n$ and $f(R) = \left( R^b - \Lambda\right)^c$ models are examined by using our dynamical system analysis. Our results show that both of two $f(R)$ models have a viable cosmological consequence identical to the analysis present in Ref.\cite{Amendola:2007nt} for the FLRW background. Contrary to Ref.\cite{Amendola:2007nt}, we discover in our models that there is an additional anisotropic and non-zero cosmological magnetic fields fixed point emerging before the present of the standard matter epoch. This means that the universe has initially isotropic stage with the intermediated epoch as the anisotropic background and it ends up with the isotropic late-time acceleration. The primordial magnetic fields play a crucial role of the shear evolutions obtained from these two models which have the same scaling of the cosmic time as $\sigma\sim t^{-\frac13}$, instead of $\sigma\sim t^{-1}$ for the absence of the primordial magnetic cases.