On the cosmology of massive bigravity

Abstract

One of the most compelling problems in the theories of standard cosmology is related to the present acceleration of the Universe. The simplest explanation consists of adding to the action of General Relativity (GR) a (cosmological) constant Λ tuned to fit with experimental data exacerbating, if possible, the old cosmological constant problem [1]. An alternative approach is to look for theories of gravity that modify GR in order to get a weaker interaction at large distances, but still retaining the good short distances behaviour of GR (see [2] for a recent review). Since GR turns out to be the unique non-linear theory of a massless spin two field, any deviation will introduce new degrees of freedom (dof). These extra dof therefore have to kick in only at cosmological scales and need to be screened below the Solar System scale [3](). An obvious modification of GR is to promote the massless spin two mediator to a massive one, hence the name of massive gravity (for a review see [5]). A massive spin two field propagates 5 dof and this statement should be retained also when non-linear self-interactions are introduced into the action. For a long time it was believed that a fully non-linear theory of massive gravity could not exist due to a 6 ghost mode that