Abstract
We study the effect of primordial black holes on the classical rate of nucleation of AdS regions within the standard electroweak vacuum. We find that the energy barrier for transitions to the new vacuum, which characterizes the exponential suppression of the nucleation rate, can be reduced significantly in the black-hole background. A precise analysis is required in order to determine whether the the existence of primordial black holes is compatible with the form of the Higgs potential at high temperature or density in the Standard Model or its extensions.
Highlights
The creation of an anti-de Sitter (AdS) bubble within asymptotically flat or de Sitter space is a problem relevant for the issue of vacuum decay
Notice that Rh(m)/(2G) coincides with m only for 2Gm/ AdS 1, while it is much smaller than m for 2Gm/ AdS 1
The magnitude of the effect for the transition to an AdS vacuum depends on the quantity that one associates with the barrier
Summary
The creation of an anti-de Sitter (AdS) bubble within asymptotically flat or de Sitter (dS) space is a problem relevant for the issue of vacuum decay. The creation is possible during inflation, when massless fields fluctuate with a characteristic scale set by the almost constant Hubble parameter Hinf This process can be viewed as a transition beyond the potential barrier in the direction of the true vacuum, which is induced by the effective Gibbons-Hawking temperature T = Hinf/2π [2]. A question that arises naturally is whether the creation of black holes during inflation or during later periods is accompagnied by the appearance of AdS bubbles around them that arise as classical fluctuations In such a scenario, the transition to the true vacuum is not a quantum phenomenon, but is triggered by the high temperature or density environment.
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