  It has recently been shown that the graviton can consistently gain a constant
mass without introducing the Boulware-Deser ghost. We propose a gravity model
where the graviton mass is set by a scalar field and prove that this model is
free of the Boulware-Deser ghost by analyzing its constraint system and showing
that two constraints arise. We also initiate the study of the model's cosmic
background evolution and tentatively discuss possible cosmological implications
of this model. In particular, we consider a simple scenario where the scalar
field setting the graviton mass is identified with the inflaton and the
graviton mass evolves from a high to a low energy scale, giving rise to the
current cosmic acceleration.
