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 $10^{13}~$GeV determined by the amplitude of the scalar fluctuation spectrum. However, in models where the inflaton potential is of the form $V \sim \phi^k$ about its minimum, the inflaton is massless for $k\ge 4$ unless a bare mass term, $\frac12 m_\phi^2 \phi^2$, 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 $T_{\rm rh}$ arising from the decay of $\phi$ into $\mathcal{H}$ through an interaction term $\mu \phi |\mathcal{H}|^2$. We perform a renormalization group analysis to determine the relative values of $\mu$ and $m_\phi$ 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 $\texttt{HiggsTools}$ public code, we find that $3.4 \times 10^6 $ GeV $\lesssim T_{\rm rh}\lesssim 3.9 \times 10^{12} $ GeV with a corresponding constraint on the inflaton bare mass $260~{\rm GeV} \lesssim m_\phi \lesssim 3.8 \times 10^{10}~{\rm GeV}$. The dependencies between $T_{\rm rh}$ and the inflaton bare mass $m_\phi$ as well as between $\mu$ and $m_\phi$ are provided.