One loop aspects of Coleman de Luccia instantons at small backreaction

Abstract: We discuss the Euclidean path integral around Coleman de Luccia instantons. We compute their contribution at the one-loop level, at leading order in the small backreaction limit. At this level of approximation, their contribution factorizes into a pure gravity and a pure matter contribution. In deriving this result, we also clarify what happens to some zero mode contributions to the path integral, once the symmetry responsible for them is broken. With these results established, we propose a formula for the decay rate of the false vacuum in terms of gravitational path integrals, and we show that our definition matches the usual quantum field theory result as $G_{N}\rightarrow0$. Lastly, we propose a prescription to study how the phase of the gravity+matter path integral changes as we change the parameters of the theory.