Spherical symmetry in a dark energy permeated space-time

TL;DR

This paper explores a spherically symmetric static space-time influenced by dark energy, modeling it as elastic strain energy, and compares theoretical predictions with solar system observations to constrain model parameters.

Contribution

It introduces a novel model of dark energy as elastic strain energy in a four-dimensional manifold and derives the metric around a spherical mass in this framework.

Findings

Derived the metric in the linear approximation for dark energy permeated space-time.

Compared the model with de Sitter space and observational data.

Established upper limits on model parameters consistent with cosmological tests.

Abstract

The properties of a spherically symmetric static space-time permeated of dark energy are worked out. Dark energy is viewed as the strain energy of an elastically deformable four dimensional manifold. The metric is worked out in the vacuum region around a central spherical mass/defect in the linear approximation. We discuss analogies and differences with the analogue in the de Sitter space time and how these competing scenarios could be differentiated on an observational ground. The comparison with the tests at the solar system scale puts upper limits to the parameters of the theory, consistent with the values obtained applying the classical cosmological tests.