Generation of the Higgs condensate and its decay after inflation

Abstract

We investigate the dynamics of the Standard Model higgswith a minimal coupling to gravity during and after inflation. Inthe regime where the Standard Model vacuum is stable, we find thatthe higgs becomes a light spectator field after about 30 efolds ofinflation, irrespectively of its initial value. Once the higgs hasbecome light, its root-mean-square value h* relaxes toequilibrium in about 85 efolds for the inflationary scale ofH* = 104 GeV and in 20 efolds for H* = 1010 GeV. Theequilibrium value is given by h* ∼ 0.36λ*−1/4H*,where λ* = 0.09…0.0005 is the higgs self coupling at thescales H* = 104…1010 GeV. We show that the main decaychannel of the higgs condensate after inflation is the resonantproduction of Standard Model gauge bosons. For a set of parameterswe find that a significant part of the condensate has decayed inbetween 340 and 630 Hubble times after the onset of higgsoscillations, depending on H* in a non-trivial way. The higgsperturbations correspond to isocurvature modes during inflation butthey could generate significant adiabatic perturbations at a laterstage for example through a modulation of the reheating stage.However, this requires that the inflaton(s) decay no later than afew hundred Hubble times after the onset of higgs oscillations.