Massive Graviton from Diffeomorphism Invariance

In this work, we undertake a comprehensive study of the functional measure of gravitational path integrals within a general framework involving non-trivial configuration spaces. As in Riemannian geometry, the integration over non-trival configuration spaces requires a metric. We examine the interplay between the functional measure and the dynamics of spacetime for general configuration-space metrics. The functional measure gives an exact contribution to the effective action at the one-loop level. We discuss the implications and phenomenological consequences of this correction, shedding light on the role of the functional measure in quantum gravity theories. In particular, we describe a mechanism in which the graviton acquires a mass from the functional measure without violating the diffeomorphism symmetry nor including Stückelberg fields. Since gauge invariance is not violated, the number of degrees of freedom goes as in general relativity. For the same reason, Boulware–Deser ghosts and the vDVZ discontinuity do not show up. The graviton thus becomes massive at the quantum level while avoiding the usual issues of massive gravity.