Phenomenological constraints on Higgs reheating

In many models of inflation, reheating is realized through a coupling between the inflaton and the Higgs boson. Often, the mass of the inflaton is of order 10¹³ GeV determined by the amplitude of the scalar fluctuation spectrum. However, in models where the inflaton potential is of the form V ∼ ϕ^k about its minimum, the inflaton is massless for k ≥ 4 unless a bare mass term, ¹ ₂ m²_ϕϕ², is present. In this case, the inflaton mass may be of order the electroweak scale and may be subject to existing collider constraints. In particular, we investigate the constraints on the inflaton mass and reheating temperature T_rh arising from the decay of ϕ into H through an interaction term μϕjHj². We perform a renormalization group analysis to determine the relative values of μ and m_ϕ such that the Higgs potential remains stable (and perturbative) at high energy. Taking into account the running of the Higgs quartic self-coupling and the experimental constraints from the LHC via the HiggsTools public code, we find that 3.4 × 10⁶ GeV ≲ T_rh ≲ 3.9 × 10¹² GeV with a corresponding constraint on the inflaton bare mass 260 GeV ≲ m_ϕ ≲ 3.8 × 10¹⁰ GeV. The dependencies between T_rh and the inflaton bare mass m_ϕ as well as between μ and m_ϕ are provided.