On stability of Friedmann-Lema\^itre-Robertson-Walker solutions in doubled geometries

TL;DR

This paper examines the stability of cosmological solutions in models with two coupled metrics of Friedmann-Lemaître-Robertson-Walker type, inspired by discrete extra-dimensional geometries, using an effective bimetric gravity framework.

Contribution

It introduces an effective gravity action coupling two metrics and analyzes the stability of standard solutions with identical metrics under perturbations.

Findings

Standard solutions are stable under small perturbations.

The effective coupling influences the stability properties.

Insights into discrete extra-dimensional models in cosmology.

Abstract

Motivated by the models of geometry with discrete spaces as additional dimensions we investigate the stability of cosmological solutions in models with two metrics of the Friedmann-Lema\^itre-Robertson-Walker type. We propose an effective gravity action that couples the two metrics in a similar manner as in the bimetric theory of gravity and analyse whether standard solutions with identical metrics are stable under small perturbations.