Non-linear bigravity and cosmic acceleration

TL;DR

This paper investigates non-linear bigravity theories with two coupled metrics, revealing their potential to explain cosmic acceleration, dark energy, and inflation through novel dynamical mechanisms and stable bi-de-Sitter solutions.

Contribution

It introduces a new framework for cosmological solutions in non-linear bigravity, highlighting the locking mechanism and proposing bigravity as a source of dark energy and inflation.

Findings

Bigravity cosmologies can stabilize in bi-de-Sitter states.

A generic feature of these models is a period of cosmic acceleration.

Bigravity may serve as a new form of dark energy with anisotropic properties.

Abstract

We explore the cosmological solutions of classes of non-linear 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.