FRW cosmology in Milgrom's bimetric theory of gravity

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.