Cosmological perturbations in gravitational energy–momentum complex

Starting from the energy–momentum of matter and gravitational field in the framework of General Relativity and Teleparallel Gravity, we obtain the energy–momentum complex in flat FRW spacetime. We show that the complex vanishes at background level considering the various prescriptions, that is the Einstein, Møller, Landau–Lifshitz and Bergmann ones. On the other hand, at level of linear cosmological perturbations, the energy–momentum complex is different from zero and coincides in the various prescriptions. Finally, we evaluate the gravitational energy for different cosmological epochs governed by non-relativistic matter, radiation, inflationary scalar fields and cosmological constant.