Abstract
We extend the study of the effect of static primordial black holes on vacuum decay. In particular, we compare the tunneling rates between vacua of different values of the cosmological constant and black hole mass by pointing out the dominant processes based on a numerical examination of the thin wall instanton. Three distinct cases are considered, namely the nucleation of a true vacuum bubble into the false vacuum, the nucleation of a false vacuum bubble into the true vacuum as well as the Farhi-Guth-Guven mechanism. As a proof of concept, it is shown that in order to increase the transition rate into an inflating region, we find that not only is the inclusion of a black hole necessary, but the inclusion of a cosmological constant in the initial phase is also required. Among the cases studied, we show that the most likely scenario is the elimination of inhomogeneities in the final phase.
Highlights
Research on false vacuum decay in quantum field theory was prompted by the work of Sydney Coleman et al [1,2,3]
We consider the Euclidean instanton approach.1. While this approach has been applied in the context of false vacuum decay [7,8], the present work extends the analysis to the nucleation of false vacuum bubbles within a low-energy true vacuum
We apply the Euclidean approach to the FGG mechanism as well and we present a relative comparison between the FGG mechanism and the tunneling upwards in the potential with a nonzero cosmological constant in both vacua
Summary
Research on false vacuum decay in quantum field theory was prompted by the work of Sydney Coleman et al [1,2,3]. Work on the topic can be found in [4,5,6], while more recent developments, motivated by the role of impurities in the decay rates of first order phase transitions, are addressed in [7,8] In the latter, it was shown that by relaxing the initial assumption of homogeneity of de-Sitter spacetime, the inclusion of black holes, as seeds of inhomogeneity, leads to enhanced decay rates. We present the most general expression for the tunneling rates of false and true vacuum bubbles with a SdS interior/exterior to determine which processes are favored due the inclusion of a cosmological constant in the initial phase. V we provide the reader with details about conical angles in Appendix A
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