Inflation and late-time cosmic acceleration in non-minimal Maxwell-$F(R)$ gravity and the generation of large-scale magnetic fields

TL;DR

This paper explores how non-minimal Maxwell-$F(R)$ gravity can drive cosmic inflation and late-time acceleration, generate large-scale magnetic fields, and remain consistent with observational constraints.

Contribution

It introduces a model where electromagnetic fields coupled to curvature induce inflation, magnetic field generation, and late-time acceleration, all consistent with current tests and free of instabilities.

Findings

Power-law inflation achieved via non-minimal coupling.

Large-scale magnetic fields generated through conformal invariance breaking.

Model consistent with solar system tests and cosmological bounds.

Abstract

We study inflation and late-time acceleration in the expansion of the universe in non-minimal electromagnetism, in which the electromagnetic field couples to the scalar curvature function. It is shown that power-law inflation can be realized due to the non-minimal gravitational coupling of the electromagnetic field, and that large-scale magnetic fields can be generated due to the breaking of the conformal invariance of the electromagnetic field through its non-minimal gravitational coupling. Furthermore, it is demonstrated that both inflation and the late-time acceleration of the universe can be realized in a modified Maxwell-$F(R)$ gravity which is consistent with solar system tests and cosmological bounds and free of instabilities. At small curvature typical for current universe the standard Maxwell theory is recovered. We also consider classically equivalent form of non-minimal Maxwell-$F(R)$ gravity, and propose the origin of the non-minimal gravitational coupling function based on renormalization-group considerations.