Extended minimal theories of massive gravity

TL;DR

This paper introduces extended minimal theories of massive gravity that maintain only two degrees of freedom, modify gravitational interactions, and have potential cosmological implications, while avoiding ghosts and instabilities.

Contribution

It develops a new class of massive gravity theories with constraints ensuring only tensor modes propagate, and explores their cosmological perturbations and phenomenology.

Findings

Gravitational waves are the only propagating degrees of freedom with non-trivial mass.

Theories allow a variable effective gravitational constant, G_eff, differing from Newton's G.

A subclass of models exhibits rich cosmological phenomenology.

Abstract

In this work, we introduce a class of extended Minimal Theories of Massive Gravity (eMTMG), without requiring a priori that the theory should admit the same homogeneous and isotropic cosmological solutions as the de Rham-Gabadadze-Tolley massive gravity. The theory is constructed as to have only two degrees of freedom in the gravity sector. In order to perform this step we first introduce a precursor theory endowed with a general graviton mass term, to which, at the level of the Hamiltonian, we add two extra constraints as to remove the unwanted degrees of freedom, which otherwise would typically lead to ghosts and/or instabilities. On analyzing the number of independent constraints and the properties of tensor mode perturbations, we see that the gravitational waves are the only propagating gravitational degrees of freedom which do acquire a non-trivial mass, as expected. In order to understand how the effective gravitational force works for this theory we then investigate cosmological scalar perturbations in the presence of a pressureless fluid. We then restrict the whole class of models by imposing the following conditions at all times: 1) it is possible to define an effective gravitational constant, $G_{{\rm eff}}$; 2) the value $G_{\text{eff}}/G_{N}$ is always finite but not always equal to unity (as to allow some non-trivial modifications of gravity, besides the massive tensorial modes); and 3) the square of mass of the graviton is always positive. These constraints automatically make also the ISW-effect contributions finite at all times. Finally we focus on a simple subclass of such theories, and show they already can give a rich and interesting phenomenology.