Evolution of gravitational waves in non-minimal coupling between geometry and matter theories of gravity

We consider some specific models of non-minimal matter-geometry coupling theories and investigate the propagation of the gravitational waves in them. Extracting the temporal evolution of the gravitational wave equation within the framework of a flat FRW universe with a perfect fluid distribution, we analyze the waveforms traveling during the time. We find that while both the amplitude and frequency of the GWs decay with time in all considered models, the rate of reduction is highly sensitive to the values of the equation of state parameter and input parameters of the considered models. & COPY; 2023 Elsevier B.V. All rights reserved.