http://arxiv.org/abs/1704.06884
In this work, we investigate the electroweak vacuum instability in the adiabatic or non-adiabatic cosmological background. In the general cosmological background, the vacuum field fluctuations $\left< { \delta \phi }^{ 2 } \right>$ grow in proportional to the cosmological scale. The large vacuum fluctuations of the Higgs field can destabilize the effective Higgs potential, or generate the catastrophic AdS domains or bubbles. These unwanted phenomena cause the catastrophic collapse of the Universe. By using the adiabatic (WKB) expansion or the adiabatic regularization methods, we obtain the exact renormalized vacuum fluctuations $\left< { \delta \phi }^{ 2 } \right>{\rm ren}$ of the Higgs field in the adiabatic and the non-adiabatic cosmological background. The non-adiabatic Higgs vacuum fluctuations generally cause the catastrophic phenomena. On the other hand, the adiabatic Higgs vacuum fluctuations have little effect on the Higgs vacuum stability. However, in the slowly-varying background by another scalar field $S$, the adiabatic Higgs vacuum fluctuations can destabilize the effective Higgs potential and provide the upper bound of the mass of the background scalar field $S$ as $m{S} \lesssim 10^{13}\ {\rm GeV}$ where we assume the instability scale $\Lambda_{I} \approx 10^{11}\ {\rm GeV}$.
K. Kohri and H. Matsui
Tue, 25 Apr 17
13/59
Comments: 16 pages