Constraints on Inflaton Higgs Field Couplings

TL;DR

This paper constrains the inflaton-Higgs couplings during reheating to prevent the Higgs field from becoming unstable, deriving bounds on coupling parameters and reheat temperature to ensure Higgs stability.

Contribution

It provides new bounds on inflaton-Higgs couplings and reheat temperature, combining semi-analytical and numerical methods to analyze Higgs stability during reheating.

Findings

Upper bounds on inflaton-Higgs couplings:  < 1.6  10^{-5} m_ or cubic and  < 10^{-8} for quartic interactions.

Reheat temperature constrained to .2  10^9 GeV to maintain Higgs stability.

Lower bounds on couplings from inflationary fluctuations, ensuring Higgs remains stabilized during inflation.

Abstract

According to the best-fit parameters of the Standard Model, the Higgs field's potential reaches a maximum at a field value $h \sim 10^{10-11}$ GeV and then turns over to negative values. During reheating after inflation, resonance between the inflaton and the Higgs can cause the Higgs to fluctuate past this maximum and run down the dangerous side of the potential if these fields couple too strongly. In this paper, we place constraints on the inflaton-Higgs couplings such that the probability of the Higgs entering the unstable regime during reheating is small. To do so, the equations of motion are approximately solved semi-analytically, then solved fully numerically. Next the growth in variance is used to determine the parameter space for $\kappa$ and $\alpha$, the coupling coefficients for inflaton-Higgs cubic and quartic interactions, respectively. We find the upper bounds of $\kappa < 1.6 \times 10^{-5} m_\phi \sim 2.2 \times 10^8$ GeV and $\alpha < 10^{-8}$ to allow the Higgs to remain stable in most Hubble patches during reheating, and we also find the full two parameter joint constraints. We find a corresponding bound on the reheat temperature of $T_\text{reh} \lesssim 9.2 \times 10^9$ GeV. Additionally, de Sitter temperature fluctuations during inflation put a lower bound on inflaton-Higgs coupling by providing an effective mass for the Higgs, pushing back its hilltop during inflation. These additional constraints provide a lower bound on $\alpha$, while $\kappa$ must also be non-zero for the inflaton to decay efficiently.