Dark Energy and Doubly Coupled Bigravity

TL;DR

This paper explores the cosmological implications and gravitational properties of doubly coupled bigravity, showing it can mimic dark energy, modify gravity on large scales, and produce observable effects like gravitational birefringence.

Contribution

It provides a detailed analysis of late-time cosmology, perturbative spectrum, and gravitational modifications in doubly coupled bigravity with a focus on observable signatures.

Findings

The universe can evolve from matter dominance to dark energy dominance with a tunable equation of state.

Gravity modifications affect structure growth and lensing, with the $\Sigma$ parameter differing from one.

The spectrum includes five scalar degrees of freedom, with two gravitons exhibiting a non-trivial mass matrix and birefringence.

Abstract

We analyse the late time cosmology and the gravitational properties of doubly coupled bigravity in the constrained vielbein formalism (equivalent to the metric formalism) when the mass of the massive graviton is of the order of the present Hubble rate. We focus on one of the two branches of background cosmology where the ratio between the scale factors of the two metrics is algebraically determined. The Universe evolves from a matter dominated epoch to a dark energy dominated era where the equation of state of dark energy can always be made close to -1 now by appropriately tuning the graviton mass. We also analyse the perturbative spectrum of the theory in the quasi static approximation well below the strong coupling scale where no instability is present and we show that there are five scalar degrees of freedom, two vectors and two gravitons. In a cosmological FRW background for both metrics, four of the five scalars are Newtonian potentials which lead to a modification of gravity on large scales. In this scalar sector, gravity is modified with effects on both the growth of structure and the lensing potential. In particular, we find that the $\Sigma$ parameter governing the Poisson equation of the weak lensing potential can differ from one in the recent past of the Universe. Overall, the nature of the modification of gravity at low energy, which reveals itself in the growth of structure and the lensing potential, is intrinsically dependent on the couplings to matter and the potential term of the vielbeins. We also find that the time variation of Newton's constant in the Jordan frame can easily satisfy the bound from solar system tests of gravity. Finally we show that the two gravitons present in the spectrum have a non-trivial mass matrix whose origin follows from the potential term of bigravity. This mixing leads to gravitational birefringence.