The effective Higgs potential and vacuum decay in Starobinsky inflation

TL;DR

This paper investigates how the combination of the Standard Model and Starobinsky inflation affects the stability of the universe's vacuum, deriving a lower bound on the Higgs-curvature coupling to ensure vacuum survival during inflation.

Contribution

It provides a novel analysis of vacuum stability in the context of Starobinsky inflation, establishing a new lower bound on the Higgs-curvature coupling parameter.

Findings

A lower bound of  0.1 on the Higgs-curvature coupling g 0 ensures vacuum stability during inflation.

The bound is stronger than in models without Higgs-inflaton coupling.

Results are sensitive to the dynamics at the end of 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 $\xi\gtrsim 0.1$ 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.