On the catalysis of the electroweak vacuum decay by black holes at high temperature

D Canko,N Tetradis,A Riotto,G Jelic-Cizmek,I Gialamas

doi:10.1140/epjc/s10052-018-5808-y

Abstract

We study the effect of primordial black holes on the classical rate of nucleation of AdS regions within the standard electroweak vacuum at high temperature. We base our analysis on the assumption that, at temperatures much higher than the Hawking temperature, the main effect of the black hole is to distort the Higgs configuration dominating the transition to the new vacuum. We estimate the barrier for the transition by the ADM mass of this configuration, computed through the temperature-corrected Higgs potential. We find that the exponential suppression of the nucleation rate can be reduced significantly, or even eliminated completely, in the black-hole background if the Standard Model Higgs is coupled to gravity through the renormalizable term xi {mathcal {R}} h^2.

Highlights

It is well-known that for the current measured values of the Higgs and top quark masses the Standard Model (SM) effective potential develops an instability
The question whether the existence of primordial black holes [41,42,43,44] is consistent with the stability of the electroweak vacuum has important implications for the compatibility of the Standard Model of particle physics and the cosmological model [45]
If the reheating temperature is larger than ∼ 10−7 MPl, Rh is too small at the onset of the radiation-dominated era for the black holes to have a significant effect on the rate

Summary

Introduction

It is well-known that for the current measured values of the Higgs and top quark masses the Standard Model (SM) effective potential develops an instability. We allow for a nonminimal coupling of the Higgs field to gravity This additional coupling can have strong effects on the action of the bounce in the case of quantum tunnelling, or the free energy of the critical bubble in the case of thermal tunnelling. Such behavior is known to occur in the context of inflation [31] and similar features are expected within the strong gravitational field of a black hole.

Equations of motion

Finite-temperature effects

Conclusions