Extended DBI massive gravity with generalized fiducial metric

TL;DR

This paper extends DBI massive gravity by generalizing the fiducial metric, allowing for all FLRW solutions, but finds issues with degrees of freedom and stability, including ghost modes.

Contribution

It introduces a generalized fiducial metric in DBI massive gravity, expanding solution space and analyzing degrees of freedom and stability issues.

Findings

All FLRW solutions are admitted, including flat, closed, and open geometries.

The model exhibits ghost degrees of freedom at small scales.

The self-accelerating branch acts as a cosmological constant for late-time acceleration.

Abstract

We consider an extended model of DBI massive gravity by generalizing the fiducial metric to be an induced metric on the brane corresponding to a domain wall moving in five-dimensional Schwarzschild-Anti-de Sitter spacetime. The model admits all solutions of FLRW metric including flat, closed and open geometries while the original one does not. The background solutions can be divided into two branches namely self-accelerating branch and normal branch. For the self-accelerating branch, the graviton mass plays the role of cosmological constant to drive the late-time acceleration of the universe. It is found that the number degrees of freedom of gravitational sector is not correct similar to the original DBI massive gravity. There are only two propagating degrees of freedom from tensor modes. For normal branch, we restrict our attention to a particular class of the solutions which provides an accelerated expansion of the universe. It is found that the number of degrees of freedom in the model is correct. However, at least one of them is ghost degree of freedom which always present at small scale implying that the theory is not stable.