# Inflation of the Universe by the Non-minimal $Y(R)F^2$ Models

## TL;DR

This paper explores how non-minimal coupling of vector fields to gravity can drive cosmic inflation, presenting exact solutions with different scale factor behaviors while maintaining isotropy.

## Contribution

It introduces a model with non-minimal $Y(R)F^2$ coupling that preserves isotropy using vector triplets or random fields, and derives exact inflationary solutions.

## Key findings

- Exact power-law inflation solutions obtained.
- Hyperbolic and hybrid scale factor solutions derived.
- Model maintains isotropy with vector fields.

## Abstract

The cosmological solutions of the non-minimal $ Y (R)F^2 $ theory which are compatible with FRW space-time are investigated. In order to avoid the isotropy violation of a vector field, it can be considered that the presence of a triplet of vector fields satisfying $SO(3)$ symmetry, or the average of randomly oriented electromagnetic fields over the sufficiently large volume. By considering the symmetry arguments, the inflation driven by the non-minimally coupled vector fields is studied. Then the cosmological solutions and corresponding models are obtained with the power law, hyperbolic and hybrid scale functions.