Higgstory repeats itself

Abstract

We consider a scalar potential with two minima, one of which is arbitrarily deep, such as could be the case for the Higgs potential in the Standard Model. A recent calculation within the thin-wall approximation [1] concludes that regions in which the scalar field takes values beyond the top of the potential barrier are forced by gravity to collapse, while they remain hidden behind a black hole horizon. We show that the thin-wall approximation is not applicable to this problem. We clarify the issue through numerical and analytical solutions to the field equations of the gravity-scalar system. We find that regions around the deeper minimum expand, and would thereby engulf the Universe in post-inflationary cosmology. We also show that black holes with Higgs hair are unstable. Even though the physics of the true vacuum is different, our final conclusion replicates the earlier ‘Higgstory’ paper [2].