Phantom crossing and quintessence limit in extended nonlinear massive gravity

We investigate the cosmological evolution in a universe governed by the extended, varying-mass, nonlinear massive gravity, in which the graviton mass is promoted to a scalar field. We find that the dynamics, both in flat and open universe, can lead the varying graviton mass to zero at late times, offering a natural explanation for its hugely constrained observed value. Despite the limit of the scenario toward standard quintessence, at early and intermediate times it gives rise to an effective dark-energy sector of a dynamical nature, which can also lie in the phantom regime, from which it always exits naturally, escaping a Big Rip. Interestingly enough, although the motivation of massive gravity is to obtain an IR modification, its varying-mass extension in cosmological frameworks leads to early and intermediate times modification instead.