Theory of stress and strain fields in general relativity and cosmological expansion

Théorie des champs des contraintes et déformations en relativité générale et expansion cosmologique.

Mathieu Beau (1)

1 STP-DIAS - School of Theoretical Physics [Dublin]

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.

Mots clés: Gravitation; relativité; théorie des champs; mécanique des milieux continus

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]; Physique Générale [physics.gen-ph]

Mathieu Beau. Théorie des champs des contraintes et déformations en relativité générale et expansion cosmologique.. 2014. ⟨hal-00683021v3⟩