Anisotropic cosmological solutions to the $Y(R)F^2$ gravity

TL;DR

This paper explores anisotropic cosmological solutions in a modified gravity theory with electromagnetic coupling, deriving exact solutions that tend toward isotropy over time.

Contribution

It provides new exact anisotropic solutions in Y(R)F^2 gravity with non-minimal electromagnetic couplings, analyzing their late-time isotropization behavior.

Findings

Solutions approach isotropy at late times

Exact solutions with hyperbolic expansion functions

Electromagnetic fields influence anisotropic evolution

Abstract

We investigate anisotropic cosmological solutions of the theory with non-minimal couplings between electromagnetic fields and gravity in $Y(R) F^2$ form. After we derive the field equations by the variational principle, we look for spatially flat cosmological solutions with magnetic fields or electric fields. Then we give exact anisotropic solutions by assuming the hyperbolic expansion functions. We observe that the solutions approach to the isotropic case in late-times.