The effective Higgs potential and vacuum decay in Starobinsky inflation

Abstract

Based on the current experimental data, the Standard Model predicts that the current vacuum state of the Universe is metastable, leading to a non-zero rate of vacuum decay through nucleation of bubbles of true vacuum. Our existence implies that there cannot have been any such bubble nucleation events anywhere in our whole past lightcone. We consider a minimal scenario of the Standard Model together with Starobinsky inflation, using three-loop renormalization group improved Higgs effective potential with one-loop curvature corrections. We show that the survival of the vacuum state through inflation places a lower bound ξ 0.1 on the non-minimal Higgs curvature coupling, the last unknown parameter of the Standard Model. This bound is significantly stronger than in single field inflation models with no Higgs-inflaton coupling. It is also sensitive to the details of the dynamics at the end of inflation, and therefore it can be improved with a more detailed study of that period.

The Stochastic Relaxion

“…• In appendix A, we presented the flux-over-population method [19] for finding the escape rate from a false minimum in our framework. Such method has been considered in cosmology for studying phase transitions in de Sitter spacetime [58], with potential application the study of vacuum survival during inflation [59]. The main result of this appendix is the analytical formula for the decay rate given in equation (A.15) (and reproduced in (3.8), that is compared with the decay rate extracted from the numerical solution to the FP equation.…”