Ruling out Critical Higgs Inflation?

TL;DR

Critical Higgs inflation, involving a rising inflection point at smaller field values, faces significant theoretical and observational challenges, making its viability questionable due to constraints from the tensor-to-scalar ratio and parameter uncertainties.

Contribution

This paper critically examines the viability of critical Higgs inflation by incorporating NNLO corrections and analyzing observational constraints, revealing significant tensions that challenge the model's feasibility.

Findings

Potential at the inflection point exceeds bounds set by current tensor-to-scalar ratio limits.

The model only remains viable at the upper edge of the strong coupling parameter range.

Critical Higgs inflation likely cannot produce dark matter black holes or sustain inflation under realistic conditions.

Abstract

We consider critical Higgs inflation, namely Higgs inflation with a rising inflection point at smaller field values than those of the plateau induced by the non-minimal coupling to gravity. It has been proposed that such configuration is compatible with the present CMB observational constraints on inflation, and also with primordial black hole production accounting for the totality or a fraction of the observed dark matter. We study the model taking into account the NNLO corrections to the Higgs effective potential: such corrections are extremely important to reduce the theoretical error associated to the calculation. We find that, in the 3 sigma window for the relevant low energy parameters, which are the strong coupling and the Higgs mass (the top mass follows by requiring an inflection point), the potential at the inflection point is so large (and so is the Hubble constant during inflation) that the present bound on the tensor-to-scalar ratio is violated. The model is viable only allowing the strong coupling to take its upper 3-4 sigma value. In our opinion, this tension shows that the model of critical Higgs inflation is likely to be not viable: neither inflation nor black holes as dark matter can be originated in this version of the model.