Troubles for Unimodular Gravity

We compute the contribution of various gravitational instantons to the path integral in the standard formulation of unimodular gravity, an alternative theory of gravity where the determinant of the metric is not dynamical. Following similar computations in General Relativity, we derive the entropy/area ratio for cosmological and black hole horizons, finding in general disagreement with General Relativity (GR) for solutions with non-zero cosmological constant. Furthermore, that ratio presents a discontinuity as Λ → 0. We also argue that unimodular gravity and General Relativity are equivalent for perturbative processes in asymptotically flat spacetimes. Finally, we present a generalized version of unimodular gravity which reproduces the full set of Einstein’s equations in the classical limit (including the trace), but which does not necessarily agree with it at the quantum level.