Cosmology of quasi-dilaton massive gravity with non-minimal kinetic coupling

In this study, we introduce an extension of the quasi-dilaton massive gravity theory and derive the field equations by varying the action with respect to the metric. This extension elucidates the dynamics of the system and demonstrates how it can encompass and recover previous cosmological models through different parameter values. We present the cosmological background equations to analyze self-accelerating solutions that can explain the late-time accelerated expansion of the Universe, driven by an effective cosmological constant arising from massive gravity. Besides, we apply the quasi-dilaton massive gravity theory with non-minimal kinetic coupling to a Type Ia Supernovae (SNIa) data set to test its viability. Our findings indicate that the theory is able to account for the observed acceleration of the expansion of the universe without invoking dark energy. In addition, we carry out a comprehensive perturbation analysis examining tensor, vector, and scalar perturbations independently. We derive the dispersion relation of gravitational waves in a Friedman-Lemaitre-Robertson-Walker (FLRW) cosmology and determine the stability conditions of the system. Such an analysis results in a sharper quasi-dilaton massive gravity theory with non-minimal kinetic coupling by ensuring the stability conditions of the system are maintained and that strong constraints on theory parameters are provided.