Mass-Varying Massive Gravity with k-essence

For a large class of mass-varying massive gravity models, the graviton mass cannot provide the late-time cosmic expansion of the universe due to its vanishing at late time. In this work, we propose a new class of mass-varying massive gravity in which the graviton mass varies according to a kinetic term of a k-essence field. By using a more general form of the fiducial metric, we found a solution such that a non-vanishing graviton mass can drive the accelerated expansion of the universe at late time. We also perform dynamical analyses of such model and found that without introducing the k-essence Lagrangian, the graviton mass can be responsible for both dark contents of the universe, namely dark energy that drives the accelerated expansion of the universe and non-relativistic matter that plays the role of dark matter. Moreover, by including the k-essence Lagrangian, we found that it is possible to alleviate the so-called cosmic coincidence problem.