Horndeski genesis: consistency of classical theory

TL;DR

This paper examines the classical consistency of Horndeski genesis models, analyzing higher-order perturbations to identify strong coupling scales and conditions for a valid classical description.

Contribution

It extends previous cubic perturbation analysis to arbitrary order, deriving conditions for classical validity in Horndeski genesis scenarios.

Findings

Identifies the strong coupling energy scales for higher-order perturbations.

Finds that the most restrictive condition matches the cubic case analysis.

Provides criteria for the classical treatment's validity in these models.

Abstract

Genesis within the Horndeski theory is one of possible scenarios for the start of the Universe. In this model, the absence of instabilities is obtained at the expense of the property that coefficients, serving as effective Planck masses, vanish in the asymptotics $t\rightarrow -\infty$, which signalizes the danger of strong coupling and inconsistency of the classical treatment. We investigate this problem in a specific model and extend the analysis of cubic action for perturbations (arXiv:2003.01202) to arbitrary order. Our study is based on power counting and dimensional analysis of the higher order terms. We derive the latter, find characteristic strong coupling energy scales and obtain the conditions for the validity of the classical description. Curiously, we find that the strongest condition is the same as that obtained in already examined cubic case.