# $F(R)$ Gravity with an Axion-like Particle: Dynamics, Gravity Waves, Late and Early-time Phenomenology

## TL;DR

This paper explores a generalized $F(R)$ gravity model coupled with an axion-like scalar, analyzing its cosmological dynamics, gravitational wave behavior, and early universe constraints, revealing potential effects on gravitational wave propagation and cosmological evolution.

## Contribution

It introduces a non-minimally coupled $F(R)$ gravity model with an axion-like particle, detailing its cosmological solutions, gravitational wave modifications, and early universe constraints.

## Key findings

- Arbitrary cosmological evolutions can be realized within the model.
- Gravitational wave speed matches $F(R)$ gravity, with possible enhancement or dissipation effects.
- Constraints from the radiation era limit the non-minimal coupling strength.

## Abstract

In this work we investigate several theoretical and phenomenological implications of a scalar -$F(R)$ gravity containing a non-minimal coupling to the scalar curvature. This kind of model is a generalization of axion-$F(R)$ gravity models, so we shall examine several implications of the latter theory. Firstly we study in detail the Einstein frame picture of the model, and also we discuss the dynamics of the cosmological system. By appropriately using the equations of motion, we demonstrate that an arbitrary cosmological evolution can be realized. Also we study the gravitational waves of the theory, and we demonstrate that the speed of their propagation is the same as in $F(R)$ gravity, but there is the possibility of enhancement or dissipation of the gravitational waves, an effect quite similar to the propagation of gravity waves in a viscous fluid. Finally, we examine the energy momentum tensor and we investigate which quantities related to it are conserved. We also present the constraints imposed by the radiation domination era on the non-minimal coupling of the axion scalar field to the scalar curvature.