Horndeski genesis: consistency of classical theory

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 → −∞, 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.

Nonsingular cosmological models with strong gravity in the past

“…Interestingly, the result of the all-order analysis of Ref. [19] coincides with the result of Ref. [18] obtained by studying the cubic order only: both lead to the same constraints on the parameters 2 .…”

“…This issue was considered in Refs. [17,18,19] in the framework of the class of models suggested in Ref. [5].…”

“…2 A would-be caveat in the analysis of Ref. [19] is that it did not give explicit comparison of strong coupling energy scales emerging at different orders of perturbation theory. The subtlety is that when the strong coupling scale inferred from a higher order term is below that coming from lower order ones, the naive estimate for the strong coupling scale may break down [21].…”

“…Another model is a combination of genesis and bounce: the Universe starts from the flat space-time, then contracts, passes through the bounce and then evolves in the same way as in the first example. For completeness, we design yet another, "standard" genesis model (in which the Universe expands from the beginning), which satisfies the condition [19] of the absence of strong coupling and thus improves on the model of Ref. [5].…”

Improved DHOST Genesis

“…One possible way to realize the NEC violation is introducing Horndeski/Generalized Galileon theory [31][32][33][34], which results in the Galileon Genesis model [35,36] (see also earlier in [37]). The physics of Galileon Genesis is studied in [38][39][40][41][42] and extended in [43][44][45][46][47][48][49][50][51][52].…”