FRW cosmology in Milgrom's bimetric theory of gravity

TL;DR

This paper explores FRW cosmological solutions within Milgrom's bimetric gravity, revealing behaviors similar to General Relativity at high acceleration and potential explanations for cosmic acceleration without dark matter at low acceleration.

Contribution

It provides the first detailed analysis of homogeneous and isotropic solutions in Milgrom's bimetric theory, highlighting conditions for cosmic acceleration and dark matter requirements.

Findings

High acceleration solutions mimic GR with a cosmological constant.

Low acceleration solutions differ significantly from GR.

Some solutions require non-baryonic dark matter or extra interactions.

Abstract

We consider spatially homogeneous and isotropic Friedmann-Robertson-Walker (FRW) solutions of Milgrom's recently proposed class of bimetric theories of gravity. These theories have two different regimes, corresponding to high and low acceleration. We find simple power-law matter dominated solutions in both, as well as solutions with spatial curvature, and exponentially expanding solutions. In the high acceleration limit these solutions behave like the FRW solutions of General Relativity, with a cosmological constant term that is of the correct order of magnitude to explain the observed accelerating expansion of the Universe. We find that solutions that remain in the high acceleration regime for their entire history, however, require non-baryonic dark matter fields, or extra interaction terms in their gravitational Lagrangian, in order to be observationally viable. The low acceleration regime also provides some scope to account for this deficit, with solutions that differ considerably from their general relativistic counterparts.