Gravitational waves in $f(R,T)$ and $f(R,T^{\varphi })$ theories of gravity

There is a host of alternative theories of gravitation in the literature, among them the $f(R,T)$ and $f(R,T^{\varphi })$ theories recently elaborated by Harko et al. In these theories, $R$, $T$ and $T^{\varphi }$ are respectively the Ricci scalar and the traces of the energy-momentum tensors of matter and of a scalar field. There is already in the literature a series of studies of different forms of the $f(R,T)$ and $f(R,T^{\varphi })$ functions as well as their cosmological consequences. However, there have been no studies so far related to gravitational waves. Here we consider such an issue, in particular, studying the putative extra polarization modes that can appear in the scope of such theories. Different functional forms of $f(R,T^{\varphi })$ are considered and the gravitational waveforms are found for the extra polarization modes in the cases in which they are present.