Gravitational waves in f(R, T)-rainbow gravity: even modes and the Huygens principle

Abstract

In the context of f(R, T)-gravity, propagation of gravitational waves (GWs) for even (or polar) modes is explored by using the Regge-Wheeler gauge in the conformally flat Friedman-Lemaitre-Robertson-Walker type rainbow (CFR) universe. Writing the perturbed field equations for the polar GWs in the CFR spacetime, we first acquire a second-order differential equation for one of the unknown perturbation factors and then get all other unknown perturbation functions. Withal, we reach a conclusion that both the four-velocity vector components except the third one and the corresponding matter distribution are affected by the polar perturbation. Furthermore, the effect of rainbow functions, which can change the geometry of space-time, on the polar GWs is also analyzed graphically. We achieve that the shape (wavelength and amplitude) of polar GWs is dramatically impressed by the alteration of rainbow functions. Lastly, we investigate whether the polar GWs satisfy the Huygens principle.