Cosmological histories in bimetric gravity: A graphical approach

TL;DR

This paper introduces a graphical method to identify viable solution branches in bimetric gravity models, enabling qualitative inference of cosmological expansion histories and their physical properties.

Contribution

It presents a novel graphical approach to analyze solution branches in bimetric gravity, aiding in understanding their cosmological implications.

Findings

Method to find viable solution branches for arbitrary parameters

Graphical analogy of scale factor ratios as a particle on a track

Qualitative inference of expansion histories in bimetric models

Abstract

The bimetric generalization of general relativity has been proven to be able to give an accelerated background expansion consistent with observations. Apart from the energy densities coupling to one or both of the metrics, the expansion will depend on the cosmological constant contribution to each of them, as well as the three parameters describing the interaction between the two metrics. Even for fixed values of these parameters can several possible solutions, so called branches, exist. Different branches can give similar background expansion histories for the observable metric, but may have different properties regarding, for example, the existence of ghosts and the rate of structure growth. In this paper, we outline a method to find viable solution branches for arbitrary parameter values. We show how possible expansion histories in bimetric gravity can be inferred qualitatively, by picturing the ratio of the scale factors of the two metrics as the spatial coordinate of a particle rolling along a frictionless track.