Domain wall solution in $F(R)$ gravity and variation of the fine structure constant

TL;DR

This paper constructs domain wall solutions within $F(R)$ gravity, explores their properties, and investigates how non-minimal electromagnetic couplings in this framework could lead to variations in the fine structure constant, with cosmological implications.

Contribution

It provides explicit $F(R)$ gravity models with domain wall solutions and analyzes the potential variation of the fine structure constant due to electromagnetic coupling in this context.

Findings

Explicit $F(R)$ models with domain walls are constructed.

Time variation of the fine structure constant may occur due to electromagnetic coupling.

Models are constrained by observational limits on the fine structure constant variation.

Abstract

We construct a domain wall solution in $F(R)$ gravity. We reconstruct a static domain wall solution in a scalar field theory. We also reconstruct an explicit $F(R)$ gravity model in which a static domain wall solution can be realized. Moreover, we show that there could exist an effective (gravitational) domain wall in the framework of $F(R)$ gravity. In addition, it is demonstrated that a logarithmic non-minimal gravitational coupling of the electromagnetic theory in $F(R)$ gravity may produce time-variation of the fine structure constant which may increase with decrease of the curvature, and that this model would be ruled out by the constraints on the time variation of the fine structure constant from quasar absorption lines. We also present cosmological consequences of the coupling of the electromagnetic field to a scalar field as well as the scalar curvature and discuss the relation between variation of the fine structure constant and the breaking of the conformal invariance of the electromagnetic field.