Abstract
The Higgs-inflaton coupling plays an important role in the Higgs field dynamics in the early Universe. Even a tiny coupling generated at loop level can have a dramatic effect on the fate of the electroweak vacuum. Such Higgs-inflaton interaction is present both at the trilinear and quartic levels in realistic reheating models. In this work, we examine the Higgs dynamics during the preheating epoch, focusing on the effects of the parametric and tachyonic resonances. We use lattice simulations and other numerical tools in our studies. We find that the resonances can induce large fluctuations of the Higgs field which destabilize the electroweak vacuum. Our considerations thus provide an upper bound on quartic and trilinear interactions between the Higgs and the inflaton. We conclude that there exists a favorable range of the couplings within which the Higgs field is stabilized during both inflation and preheating epochs.
Highlights
With the upper bound coming from the requirement that the Higgs-inflaton interaction preserve flatness of the inflaton potential, and the lower limit dictated by the condition that the Higgs effective mass be greater than the Hubble rate during inflation
The resulting mixed parametric-tachyonic resonance is described by the Whittaker-Hill equation
We have analyzed the issue of electroweak vacuum stability during the preheating epoch assuming that the Higgs self-coupling turns negative at high energies
Summary
We study the Higgs production within the simple m2φ2 chaotic inflation model with m = 1.3 × 10−6MPl, MPl = 1.22 × 1019 GeV ,. Not long after the end of inflation, the inflaton field undergoes oscillations φ(t) = Φ(t) cos mt. Since the consequent effective Higgs mass term can have either sign ∝ σhφφ, the tachyonic resonance becomes effective. Both of the resonances play an important role and will be studied . Where h2 plays the role of the relevant energy scale at which the coupling should be evaluated. Where hScM ∼ 1010 GeV is the critical scale of the Standard Model at which λh flips sign
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