Abstract
We study the nonperturbative dynamics of the Standard Model (SM) after inflation, in the regime where the SM is decoupled from (or weakly coupled to) the inflationary sector. We use classical lattice simulations in an expanding box in (3+1) dimensions, modeling the SM gauge interactions with both global and Abelian-Higgs analogue scenarios. We consider different post-inflationary expansion rates. During inflation, the Higgs forms a condensate, which starts oscillating soon after inflation ends. Via nonperturbative effects, the oscillations lead to a fast decay of the Higgs into the SM species, transferring most of the energy into $Z$ and $W^{\pm}$ bosons. All species are initially excited far away from equilibrium, but their interactions lead them into a stationary stage, with exact equipartition among the different energy components. From there on the system eventually reaches equilibrium. We have characterized in detail, in the different expansion histories considered, the evolution of the Higgs and of its dominant decay products, until equipartition is established. We provide a useful mapping between simulations with different parameters, from where we derive a master formula for the Higgs decay time, as a function of the coupling constants, Higgs initial amplitude and postinflationary expansion rate.
Highlights
Inflation, an early period of accelerated expansion, is the leading framework to explain the initial conditions of the Universe
We study the nonperturbative dynamics of the standard model (SM) after inflation, in the regime where the SM is decoupled from the inflationary sector
In the regime where the EW vacuum is stable with the Higgs self-coupling kept positive, the Higgs develops a large vacuum expectation value (VEV) during inflation, representing a classical condensate, homogeneous over scales exponentially larger than the inflationary radius 1=HÃ
Summary
An early period of accelerated expansion, is the leading framework to explain the initial conditions of the Universe. We will consider that the Higgs amplitude during inflation remains always in the “safe” side of the effective potential, where λðμÞ is positive This can be guaranteed if μþ is sufficiently large (compared to the inflationary scale), or alternatively, if beyond-the-SM physics stabilizes the potential at high energies. The crucial ingredient for our analysis is, not that the Higgs self-coupling λðμÞ remains positive during inflation, but the fact that the Higgs develops a vacuum expectation value (VEV) during inflation much larger than the electroweak (EW) scale ∼Oð102Þ GeV The way such condensate is attained is mostly irrelevant. Even if there is an inflaton-Higgs effective coupling, we will assume in practice that its effect is negligible, with the possible Higgs-inflaton interactions not affecting the Higgs dynamics during or after inflation Under these circumstances, the Higgs amplitude during inflation “performs” a random walk at superhorizon scales, reaching very quickly, within few e-folds, the equilibrium distribution [20]
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