Propagation of axial gravitational waves in Rastall gravity

Abstract

We discuss propagation of the axial gravitational waves (AGWs) in the spatially flat conformal Friedmann–Lemaitre–Robertson–Walker (FLRW) spacetime, which is dominated by a perfect fluid, in the generalized Rastall theory of gravity (gRT). On this purpose, we perturb the spatially flat metric, background material content and the four-velocity components with the help of Regge–Wheeler perturbations inducing AGWs and formulate the corresponding field equations for both unperturbed and perturbed metrics. Then, we focus on these equations to discuss evolution of the perturbation parameters in the radiation as well as the dust, stiff-fluid and the dark energy dominated phases of the cosmos. We see that material distribution of the background geometry does not feel the propagation of axial modes and the AGWs can produce changes in the velocity components similar to the general relativity (GR) case. As a result, we conclude that the matter-curvature coupling changes the evolution of perturbation parameters and thus the propagation of AGWs and their amplitudes.