Cosmological perturbations in gravitational energy–momentum complex

Abstract

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.

Gravitational energy-momentum pseudo-tensor in Palatini and metric $f(R)$ gravity

“…Considering a flat FLRW spacetime, we found that the energy density complex vanishes in the metric formulation of f (R) gravity. Similar results have been achieved in GR and in teleparallel gravity [3][4][5][6][7]17]. On the other hand, the complex is non-vanishing in the f (R) Palatini formulation except for the case f (R) = R. This fact could be relevant in discriminating among theories, in particular in view of gravitational radiation where the energymomentum complex can play an important role.…”

“…However, a generally accepted definition for localized gravitational energy does not exist. For example, in cosmology, it has been shown that the energy complex leads to vanishing values for open and closed Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes [3][4][5][6][7] and, in general, the problem of a correct definition of energy complex could be strictly related to the dark side issue. In this perspective, also modified gravity theories contribute to the debate in the sense that dynamical effects of dark components could be addressed by geometrical extensions or modifications of GR without invoking new particle counterparts, beyond the Standard Model, up to now not detected at fundamental level.…”

Localization of Energy and Momentum in an Asymptotically Reissner-Nordström Non-Singular Black Hole Space-Time Geometry

“…Finally, some very interesting results regarding the energy-momentum localization problem and its treatment by energy-momentum complexes are obtained in [59]. The authors investigate the gravitational energy localization in the context of both the GR and TEGR formalisms.…”

Definition of Complexity Factor for Self-Gravitating Systems in Palatini $f(R)$ Gravity

“…We shall take a model known widely as Gokhroo-Mehra ansatz (GMA). Abedi et al [62] explored the energy-momentum complex for the flat Friedmann-Robertson-Walker manifold within an environment of GR and one of the modified gravity models. It is worthy to stress that our calculated CF could be related to the energy-momentum complex because it depends on the stress-energy momentum tensor.…”