# Cosmological perturbations in gravitational energy-momentum complex

## TL;DR

This paper investigates the gravitational energy-momentum complex in flat FRW spacetime within General Relativity and Teleparallel Gravity, revealing it vanishes at background level but is non-zero at linear perturbations, with applications across cosmological epochs.

## Contribution

It provides a detailed analysis of the energy-momentum complex in cosmological models, comparing different prescriptions and extending understanding of gravitational energy in perturbative regimes.

## Key findings

- Complex vanishes at background level across prescriptions.
- At linear perturbations, the complex is non-zero and consistent across prescriptions.
- Gravitational energy evaluated for various cosmological epochs.

## 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, M{\o}ller, 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.