Stable Cosmology from Minimal Theory of Mass-Varying Massive Gravity

We study cosmological perturbations in the minimal theory of mass-varying massive gravity (MTMVMG), a constrained extension of mass-varying massive gravity that propagates only three physical degrees of freedom. We show that MTMVMG admits a stable cosmological solutions i.e. free from ghost, gradient, and tachyonic instabilities around the homogeneous and isotropic background. We further demonstrate that the dynamical external scalar field$\text{textendash}\text{textendash}$which is responsible for the mass of the graviton$\text{textendash}\text{textendash}$can suitably serve as either dark energy or the inflaton, yielding a description consistent with current cosmological observations.