On the distribution of gravitational energy in the de Sitter space

TL;DR

This paper calculates the gravitational energy distribution in de Sitter space using teleparallel gravity, revealing energy concentration near the cosmological horizon and its dependence on the cosmological constant.

Contribution

It provides a novel calculation of gravitational energy in de Sitter space within the teleparallel framework, highlighting energy localization near the horizon.

Findings

Gravitational energy is confined within the cosmological horizon.

Energy concentration increases as the cosmological constant decreases.

Results align with the phenomenology of radial acceleration in de Sitter space.

Abstract

We calculate the total gravitational energy and the gravitational energy density of the de Sitter space using the definition of localized energy that arises in the framework of the teleparallel equivalent of general relativity. We find that the gravitational energy can only be defined within the cosmological horizon and is largely concentrated in regions far from the center of spherical symmetry, i.e., in the vicinity of the maximal spacelike radial coordinate $R=\sqrt{ 3 \over \Lambda}$. The smaller the cosmological constant, the farther the concentration of energy. This result complies with the phenomenological features of the de Sitter space, namely, the existence of a radial acceleration directed away from the center of symmetry experienced by a test particle in the de Sitter space. Einstein already contemplated the de Sitter solution as a world with a surface distribution of matter, a picture that is in agreement with the present analysis.