Instability of the Electroweak Vacuum in Starobinsky Inflation

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.

22 pages, 6 figures

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Cited by in corpus (6)

• Dark matter production via a non-minimal coupling to gravity
• No-scale Brans-Dicke Gravity -- ultralight scalar boson & heavy inflaton
• Gravitational waves from a curvature-induced phase transition of a Higgs-portal dark matter sector
• Non-Scaling Topological Defects and Gravitational Waves in Higgs Portal
• Higgs vacuum metastability in $R+R^2$ gravity
• The effective Higgs potential and vacuum decay in Starobinsky inflation