Nonlinear bigravity and cosmic acceleration

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Abstract
We explore the cosmological solutions of classes of nonlinear bigravity theories. These theories are defined by effective four-dimensional Lagrangians describing the coupled dynamics of two metric tensors, and containing, in the linearized limit, both a massless graviton and an ultralight one. We focus on two paradigmatic cases: the case where the coupling between the two metrics is given by a Pauli-Fierz-type mass potential, and the case where this coupling derives from five-dimensional brane constructions. We find that cosmological evolutions in bigravity theories can be described in terms of the dynamics of two “relativistic particles,” moving in a curved Lorenzian space, and connected by some type of nonlinear “spring.” Classes of bigravity cosmological evolutions exhibit a “locking” mechanism under which the two metrics ultimately stabilize in a bi–de Sitter configuration, with relative (constant) expansion rates. In the absence of matter, we find that a generic feature of bigravity cosmologies is to exhibit a period of cosmic acceleration. This leads us to propose bigravity as a source of a new type of dark energy (“tensor quintessence”), exhibiting specific anisotropic features. Bigravity could also have been the source of primordial inflation.