Generalized Galileons: instabilities of bouncing and Genesis cosmologies and modified Genesis

Abstract

We study spatially flat bouncing cosmologies and models with the early-time Genesis epoch in a popular class of generalized Galileon theories. We ask whether there exist solutions of these types which are free of gradient and ghost instabilities. We find that irrespectively of the forms of the Lagrangian functions, the bouncing models either are plagued with these instabilities or have singularities. The same result holds for the original Genesis model and its variants in which the scale factor tends to a constant as t → −∞. The result remains valid in theories with additional matter that obeys the Null Energy Condition and interacts with the Galileon only gravitationally. We propose a modified Genesis model which evades our no-go argument and give an explicit example of healthy cosmology that connects the modified Genesis epoch with kination (the epoch still driven by the Galileon field, which is a conventional massless scalar field at that stage).

A covariant Lagrangian for stable nonsingular bounce

“…Recently, this observation has been proved, up to the cubic Galileon theory [6] and the Horndeski theory [7]. Based on the effective field theory (EFT) of nonsingular cosmologies [8][9][10], this No-go result has been more clearly illustrated.…”

“…The ghost-free nonsingular bounce is set by P (φ, X), while c 2 s ≃ 1 is set by using suitable f 1 and f 2 in (2.1). As a specific model, we set P (φ, X) in (3.1) as 6) where the potential is ekpyrotic-like…”

The Effective Field Theory of nonsingular cosmology

“…As matter of fact, by mapping the cubic Galileon to the EFT [41], eq. (2.10) will lead to the key inequality used to prove the LMR no-go theorem [33] (see the following part of this subsection); and by mapping the whole Horndeski theory to the EFT [41], eq. (2.10) will produce the key inequality in Kobayashi's paper [35].…”

“…So we have reformulated the LMR no-go theorem [33] for the cubic Galileon in the framework of EFT, which indicates the pathologies in nonsingular cosmological models based on the cubic Galileon are inevitable.…”

“…Recently, Libanov, Mironov and Rubakov (LMR) have proved a no-go theorem, which shows that healthy nonsingular cosmological models based on the cubic Galileon does not exist [33]. Hereafter, it was generalized with an additional scalar in ref.…”