Aether-quasi-dilaton massive gravity

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.

Automated summary

In this work, we extend the quasi-dilaton massive gravity theory by including the aether field. We demonstrate the existence of exact self-accelerating solutions in flat Friedmann-Lemaitre-Robertson-Walker geometry, characterized by an effective cosmological constant. Through perturbation analysis, we investigate the stability conditions for gravitational waves and the vector and scalar perturbations, showing the regions in the parameter space where the obtained solutions are free from ghost instabilities and strong coupling problem.