On post-inflation validity of perturbation theory in Horndeski scalar-tensor models

TL;DR

This paper investigates the behavior of perturbations in Horndeski scalar-tensor models after inflation, revealing conditions under which inflationary predictions remain valid despite potential growth of the Newtonian potential.

Contribution

It provides a detailed analysis of post-inflation perturbation dynamics in Horndeski theories, including a concrete example with Higgs inflation, highlighting conditions for preserving inflationary predictions.

Findings

Super-horizon Newtonian potential can grow large after inflation in Horndeski models.

Inflationary predictions remain valid if the system stays in the linear regime.

The Newtonian potential converges to a constant related to inflationary curvature perturbations.

Abstract

By using the newtonian gauge, we re-confirm that, as in the minimal case, the re-scaled Mukhanov-Sasaki variable is conserved leading to a constraint equation for the Newtonian potential. However, conversely to the minimal case, in Horndeski theories, the super-horizon Newtonian potential can potentially grow to very large values after inflation exit. If that happens, inflationary predictability is lost during the oscillating period. When this does not happen, the perturbations generated during inflation can be standardly related to the CMB, if the theory chosen is minimal at low energies. As a concrete example, we analytically and numerically discuss the new Higgs inflationary case. There, the Inflaton is the Higgs boson that is non-minimally kinetically coupled to gravity. During the high-energy part of the post-inflationary oscillations, the system is anisotropic and the Newtonian potential is largely amplified. Thanks to the smallness of today's amplitude of curvature perturbations, however, the system stays in the linear regime, so that inflationary predictions are not lost. At low energies, when the system relaxes to the minimal case, the anisotropies disappear and the Newtonian potential converges to a constant value. We show that the constant value to which the Newtonian potential converges is related to the frozen part of curvature perturbations during inflation, precisely like in the minimal case.