Higgs Inflation Using the Unstable Standard Model Potential

Abstract

It is likely that the Higgs potential of the Standard Model is unstable, turning negative at $\phi < \Lambda \sim 10^{10}$ GeV. Here we consider whether it is possible to have Higgs Inflation on the positive stable region of the potential at $\phi < \Lambda$. To do this we add a non-minimally coupled induced gravity sector with scalar $\chi$ to the Standard Model. For an appropriate form for the non-minimal coupling of $\chi$, we show that it is possible to have conventional Higgs inflation at small $\phi < \Lambda$ if the effective Planck mass in the Jordan frame during inflation is sufficiently small, with a phase transition to $\chi \neq 0$ at the end of Higgs inflation which increases the Jordan frame Planck mass to its presently observed value. In the Einstein frame this corresponds to a suppression of the Higgs kinetic and potential term at the end of inflation. We show that the predictions of Higgs inflation at tree level are unaltered from conventional Higgs Inflation, with the exception of the magnitude of the Higgs field during inflation. Hence Higgs Inflation can be achieved using the potential of the unmodified Standard Model.