Massive Cosmologies

TL;DR

This paper investigates cosmological solutions in a Lorentz-invariant massive gravity theory, finding that homogeneous and isotropic solutions are generally prohibited but can approximate the universe's evolution within certain domains, leading to bounds on the graviton mass.

Contribution

It demonstrates that the same constraint removing the Boulware-Deser ghost also forbids homogeneous and isotropic cosmologies, except in limited domains, and derives bounds on the graviton mass.

Findings

Homogeneous and isotropic solutions are prohibited globally but exist approximately in finite domains.

At high densities, solutions closely follow standard FRW cosmology.

An upper bound on the graviton mass is estimated to be below the current Hubble parameter.

Abstract

We explore the cosmological solutions of a recently proposed extension of General Relativity with a Lorentz-invariant mass term. We show that the same constraint that removes the Boulware-Deser ghost in this theory also prohibits the existence of homogeneous and isotropic cosmological solutions. Nevertheless, within domains of the size of inverse graviton mass we find approximately homogeneous and isotropic solutions that can well describe the past and present of the Universe. At energy densities above a certain crossover value, these solutions approximate the standard FRW evolution with great accuracy. As the Universe evolves and density drops below the crossover value the inhomogeneities become more and more pronounced. In the low density regime each domain of the size of the inverse graviton mass has essentially non-FRW cosmology. This scenario imposes an upper bound on the graviton mass, which we roughly estimate to be an order of magnitude below the present-day value of the Hubble parameter. The bound becomes especially restrictive if one utilizes an exact self-accelerated solution that this theory offers. Although the above are robust predictions of massive gravity with an explicit mass term, we point out that if the mass parameter emerges from some additional scalar field condensation, the constraint no longer forbids the homogeneous and isotropic cosmologies. In the latter case, there will exist an extra light scalar field at cosmological scales, which is screened by the Vainshtein mechanism at shorter distances.