Geometric sigma model of the Universe

TL;DR

This paper demonstrates how geometric sigma models can be constructed to make any chosen background universe a stable solution, providing a flexible framework for modeling different cosmological backgrounds.

Contribution

It introduces a method to tailor geometric sigma models to any background universe, ensuring classical stability of perturbations, which is a novel approach in cosmological modeling.

Findings

Any background geometry can be made a stable solution.

Small perturbations around the background are classically stable.

Three specific universe models are explicitly constructed.

Abstract

The purpose of this work is to demonstrate how an arbitrarily chosen background of the Universe can be made a solution of a simple geometric sigma model. Geometric sigma models are purely geometric theories in which spacetime coordinates are seen as scalar fields coupled to gravity. Although they look like ordinary sigma models, they have the peculiarity that their complete matter content can be gauged away. The remaining geometric theory possesses a background solution that is predefined in the process of constructing the theory. The fact that background configuration is specified in advance is another peculiarity of geometric sigma models. In this paper, I construct geometric sigma models based on different background geometries of the Universe. Whatever background geometry is chosen, the dynamics of its small perturbations is shown to posses a generic classical stability. This way, any freely chosen background metric is made a stable solution of a simple model. Three particular models of the Universe are considered as examples of how this is done in practice.