Mimetic Massive Gravity: Beyond Linear Approximation

TL;DR

This paper introduces a ghost-free massive gravity theory where the graviton mass arises via a BEH mechanism involving mimetic gravity, analyzing its perturbations, strong coupling scales, and potential dark matter implications.

Contribution

It proposes a novel massive gravity model with a non-Fierz-Pauli mass term, eliminating ghosts and exploring nonlinear effects and dark matter roles of mimetic matter.

Findings

Boulware-Deser ghost is absent to all orders.

Nonlinear corrections become significant at a scale of order m^{-1/2}.

Mimetic matter behaves as cold particles and may explain dark matter.

Abstract

We present a theory of ghost-free massive gravity where the mass of the graviton is generated through the Brout-Englert-Higgs (BEH) mechanism and one of the four scalar fields used is that of mimetic gravity. The mass term is not of the Fierz-Pauli type and the constraint eliminates the Boulware-Deser ghost which is absent to all orders. We perform a detailed analysis using the methods of cosmological perturbation theory and consider quantum fluctuations of the degrees of freedom of massive graviton and mimetic matter. It is shown that for three of the degrees of freedom of the graviton of mass $m$ the nonlinear corrections become comparable to the linear terms already at a length scale of order $m^{-\frac{1}{2}}$. Thus, at smaller scales they become strongly coupled and the graviton remains with two transverse degrees of freedom which get strongly coupled only at Planck scale. The mimetic field behaves as cold particles of half of the graviton mass and could well explain the source of dark matter in our universe. In the weakly coupled domain mimetic matter is completely decoupled from the massive graviton.