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

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 $$\delta R$$ δR and $$\delta \rho $$ δρ