Initial conditions for critical Higgs inflation

Abstract

It has been pointed out that a large non-minimal coupling ξ between the Higgs and the Ricci scalar can source higher derivative operators, which may change the predictions of Higgs inflation. A variant, called critical Higgs inflation, employs the near-criticality of the top mass to introduce an inflection point in the potential and lower drastically the value of ξ. We here study whether critical Higgs inflation can occur even if the pre-inflationary initial conditions do not satisfy the slow-roll behavior (retaining translation and rotation symmetries). A positive answer is found: inflation turns out to be an attractor and therefore no fine-tuning of the initial conditions is necessary. A very large initial Higgs time-derivative (as compared to the potential energy density) is compensated by a moderate increase in the initial field value. These conclusions are reached by solving the exact Higgs equation without using the slow-roll approximation. This also allows us to consistently treat the inflection point, where the standard slow-roll approximation breaks down. Here we make use of an approach that is independent of the UV completion of gravity, by taking initial conditions that always involve sub-planckian energies. Keywords: Inflation, Higgs boson, Standard Model