Abstract
We present a calculation of thick-wall Coleman-de-Luccia (CdL) bounces in the Standard Model effective potential in a de Sitter background. The calculation is performed including the effect of the bounce back-reaction on the metric, which we compare with the case of a fixed de-Sitter background, and with similar full-backreaction calculation in a model polynomial potential. The results show that the Standard Model potential exhibits non-trivial behavior: rather than a single CdL solution, there are multiple (non-oscillating) bounce solutions which may contribute to the decay rate. All the extra solutions found have higher actions than the largest amplitude solution, and thus would not contribute significantly to the decay rate, but their existence demonstrates that CdL solutions in the Standard Model potential are not unique, and the existence of additional, lower action, solutions cannot be ruled out. This suggests that a better understanding of the appearance and disappearance of CdL solutions in de Sitter space is needed to fully understand the vacuum instability issue in the Standard Model.
Highlights
One of the questions raised by the discovery of the Higgs boson [1,2] has been the implications it has for the stability of the electroweak vacuum
In all the cases we studied, the action of the extra solutions was found to be larger than the largest amplitude Coleman-de Luccia (CdL) solution
The most practical conclusion that can be drawn from these results is that the largest amplitude CdL solution has almost identical action to the V0 1⁄4 0 bounce, and this action depends only very weakly on the Hubble rate
Summary
One of the questions raised by the discovery of the Higgs boson [1,2] has been the implications it has for the stability of the electroweak vacuum. The possibility that the electroweak vacuum might be metastable and vulnerable to spontaneous nucleation of true-vacuum bubbles via quantum tunneling was considered even before the discovery of the Higgs boson [3], but the measurements of a Higgs mass around Mh 1⁄4 125.09 Æ 0.25 GeV and top quark mass of 173.21 GeV [4] suggest that this may be the real situation in the standard model. Of particular note is that these measurements place the Higgs boson in a narrow region of parameter space for which the electroweak vacuum is neither completely stable, nor so unstable that it should have already decayed in the lifetime of the Universe [5]. Vacuum instability in a Minkowski background has been investigated extensively (see Refs. [5,6,7] for example) and the effects of gravitational backreaction of the vacuum bubbles have been studied by many authors [8,9,10,11,12]
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