# Gravitational waves in theories with a non-minimal curvature-matter coupling

## TL;DR

This paper investigates gravitational waves in theories with non-minimal curvature-matter coupling, analyzing their properties and differences from standard models using perturbation and Newman-Penrose formalisms, with implications for cosmology.

## Contribution

It provides a detailed analysis of gravitational wave propagation in non-minimal curvature-matter coupling theories, including the effects of different matter sources and the emergence of scalar modes.

## Key findings

- Consistency with $f(R)$ theories when using a cosmological constant
- Differences in tensor mode propagation with a dark energy-like fluid
- Identification of scalar modes as mixtures of $\, ext{delta} R$ and $\, ext{delta}
ho$

## Abstract

Gravitational waves in the presence of a non-minimal curvature-matter coupling are analysed, both in the Newman-Penrose and perturbation theory formalisms. Considering a cosmological constant as a source, the non-minimally coupled matter-curvature model reduces to $f(R)$ theories. This is in good agreement with the most recent data. Furthermore, a dark energy-like fluid is briefly considered, where the propagation equation for the tensor modes differs from the previous scenario, in that the scalar mode equation has an extra term, which can be interpreted as the longitudinal mode being the result of the mixture of two fundamental excitations $\delta R$ and $\delta \rho$.