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arXiv · 2206.05926

Instability of the Electroweak Vacuum in Starobinsky Inflation

Qiang Li·Takeo Moroi·Kazunori Nakayama·Wen Yin
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Abstract

We study the stability of the electroweak vacuum during and after the Starobinsky inflation, assuming the existence of the non-minimal Higgs coupling to the Ricci scalar. In the Starobinsky inflation, there exists $R^2$ term (with $R$ being the Ricci scalar), which modifies the evolution equation of the Higgs field. We consider the case that the non-minimal coupling is sizable so that the quantum fluctuation of the Higgs field is suppressed and that the Higgs amplitude is settled near the origin during the inflation. In such a case, the Higgs amplitude may be amplified in the preheating epoch after inflation because of the parametric resonance due to the non-minimal coupling. We perform a detailed analysis of the evolution of the Higgs field in the preheating epoch by a numerical lattice simulation and derive an upper bound on the non-minimal coupling constant $\xi$ in order to realize the electroweak vacuum in the present universe. We find that the upper bound on $\xi$ in the Starobinsky inflation model is more stringent than that in conventional inflation models without the $R^2$ term.

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Qiang Li, Takeo Moroi, Kazunori Nakayama, Wen Yin. 2022-06-13. Instability of the Electroweak Vacuum in Starobinsky Inflation. https://doi.org/10.1007/jhep09(2022)102

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