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Backreaction of particle production on false vacuum decay

As originally described by Rubakov, particles are produced during the tunneling of a metastable quantum field. We propose to extend his formalism to compute the backreaction of these particles on the semiclassical decay probability of the field. The idea is to integrate out the external bath of particles by computing the reduced density matrix of the system. Following this approach, we derive an explicit correction factor in the specific case of scalar particle production in flat spacetime. In this given framework, we conclude that the backreaction is ultraviolet finite and enhances the decay rate. Moreover, in the weak production limit, the backreaction factor is directly given by one half of the total number of created particles. In order to estimate the importance of this correction, we apply our formalism to a toy model potential which allows us to consider both the decay of a homogeneous bounce and the nucleation of a thin-wall bubble. In the former case, the impact of the created particles is parameter dependent and we exhibit a reasonable choice of variables for which ones the backreaction is significant. In the latter case, we conclude that the backreaction is always negligible.