Aether-quasi-dilaton massive gravity

TL;DR

This paper extends quasi-dilaton massive gravity by including an aether field, resulting in stable, self-accelerating solutions free from ghost instabilities and strong coupling issues, with detailed perturbation analysis confirming stability.

Contribution

The work introduces an aether field extension to quasi-dilaton massive gravity, addressing instabilities and strong coupling problems while maintaining self-accelerating solutions.

Findings

Existence of exact self-accelerating solutions with an effective cosmological constant.

Identification of parameter regions free from ghost and strong coupling instabilities.

Aether field's crucial role in stabilizing perturbations despite minimal impact on background solutions.

Abstract

Although quasi-dilaton massive gravity is a well-defined gravitational theory, it exhibits instabilities and suffers from the strong coupling problem. In this work we construct an extension of the theory, through the inclusion of the aether field. Focusing on flat Friedmann-Lemaitre-Robertson-Walker geometry, we show the existence of exact, self-accelerating solutions at the background level, characterized by an effective cosmological constant arising from the graviton mass. Additionally, we perform a detailed perturbation analysis, investigating separately the tensor, vector, and scalar perturbations, extracting the dispersion relation of gravitational waves, and determining the stability conditions for vector and scalar sectors. As we show, there are always regions in the parameter space in which the obtained solutions are free from ghost instabilities, as well as from the strong coupling problem. Hence, although the aether field does not play an important role in the background self-accelerating solutions, it does play a crucial role in the alleviation of the perturbation-related problems of the simple quasi-dilaton massive gravity.