Initial Conditions for Critical Higgs Inflation

TL;DR

This paper demonstrates that critical Higgs inflation can naturally occur without fine-tuned initial conditions, as inflation acts as an attractor even with large initial Higgs velocities, using exact equations beyond slow-roll approximations.

Contribution

It shows that critical Higgs inflation is robust against a wide range of initial conditions, including large Higgs velocities, by solving the exact Higgs equations without slow-roll assumptions.

Findings

Inflation is an attractor for various initial conditions.

Large initial Higgs velocities can be compensated by initial field values.

The approach is independent of UV completion, using sub-Planckian initial energies.

Abstract

It has been pointed out that a large non-minimal coupling $\xi$ 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 $\xi$. We here study whether critical Higgs inflation can occur even if the pre-inflationary initial conditions do not satisfy the slow-roll behaviour (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 treat consistently 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.