Eternal Inflation and Reheating in the Presence of the Standard Model Higgs Field

TL;DR

This paper investigates eternal inflation with the Standard Model Higgs field, analyzing the steady state distribution, stability, and reheating effects, and establishes bounds on the inflationary Hubble scale to ensure universe stability.

Contribution

It provides a detailed calculation of the Higgs field distribution during eternal inflation using a new integral evolution method within the Standard Model framework.

Findings

Steady state Higgs distribution computed with integral evolution technique.

Bound on inflationary Hubble scale: H ≲ 10^9 GeV for observable universe.

Thermal bubble production rate is negligibly small post-inflation.

Abstract

We study the details of eternal inflation in the presence of a spectator Higgs field within the framework of the minimal Standard Model. We have recently shown that in the presence of scalar field(s) which allow inflation only within a finite domain of field values, the universe reaches a steady state where the normalized distribution for the field(s) converges to a steady state distribution [1]. In this paper, we analyze this eternal inflation scenario with the renormalized Standard Model Higgs potential, since it also allows inflation in a finite domain, but turns over at high scales due to the running of the self-coupling, marking an exit from inflation. We compute the full steady state distribution for the Higgs using an integral evolution technique that we formulated in [1] and the fractal dimension of the universe. We then obtain a bound on the inflationary Hubble scale in order to have a large observable universe contained within the instability scale of $H\lesssim\mathcal{O}(10^9)$GeV depending on the top mass. Upon reheating of the universe, thermal fluctuations in the Higgs field could potentially pose another problem; however, we compute the rate of thermal bubble production and find that the probability of tunneling in the post-inflationary era is negligibly small even for very high reheat temperatures.