Constraining the Higgs curvature coupling from vacuum decay during inflation

Abstract

According to the current experimental data, the Higgs vacuum appears to be metastable due to the development of a second, lower ground state in its potential. Consequently, this leads to a non-zero rate of vacuum decay through nucleation of bubbles of true vacuum with catastrophic consequences for our false vacuum Universe. Since such an event would render our Universe incompatible with measurements, there cannot have been any such bubble nucleation events anywhere in our whole past lightcone. Thus, we are motivated to study possible stabilising mechanisms in the early universe, focusing on the period of cosmological inflation. We consider a minimal scenario of the Standard Model of particle physics together with single-field, high-scale inflation, while accounting for the time-dependence of the Hubble rate, both in the geometry of our past light-cone and in the Higgs effective potential. The latter is approximated with three- loop renormalization group improvement supplemented with one-loop curvature corrections in de Sitter. We study three one-parameter inflationary models in field theory, quadratic, quartic, and Starobinsky-like power law inflation, and the modified gravity scenario $R + R^2$, that leads to the observationally favoured model of Starobinsky inflation. We show that the survival of the vacuum state through inflation places lower bounds on the non-minimal Higgs curvature coupling ξ, the last unknown parameter of the Standard Model. The bounds are significantly stronger in Starobinsky inflation than in field theory models with no Higgs-inflaton coupling, $\xi \gtrsim 0.1 > 0.06$ , but are independent of the duration of inflation. However, they are sensitive to the details of the dynamics at the end of inflation, and therefore they can be improved with a more detailed study of that period.