Th\'eorie des champs des contraintes et d\'eformations en relativit\'e g\'en\'erale et expansion cosmologique: Theory of stress and strain fields in general relativity and cosmological expansion

TL;DR

This paper extends general relativity by incorporating stress-energy tensors with elastic properties, deriving modified cosmological equations that include new parameters related to material properties of the universe.

Contribution

It introduces a novel approach by adding elastic stress-energy components to Einstein's equations, leading to modified Friedmann equations with additional parameters.

Findings

Modified Friedmann equations with elastic stress contributions

Relation of cosmological constant to elastic properties

Second-order corrections depending on new parameters

Abstract

In this article we propose to add stress-energy tensor to the Einstein equations, assuming that the matter-energy and the metric space-time is nothing but a continuous medium with some elastic properties. We first give a general expression of the stress tensor which is linearly related to the strain tensor. Then, we give the particular expression of the stress tensor for a spatially homnogeneous and isotropic cosmological medium. After that we derive the modified Friedmann equations. In first approximation, we end up with the usual term $\Lambda g_{\mu\nu}$ , where the cosmological constant $\Lambda=K\varepsilon$ is related with the bulk modulus K and the relative variation of volume (dilatation). Then we derive corrections to the standard model in second approximation, which depend on these two new parameters.