The Effective Field Theory of nonsingular cosmology

Abstract

In this paper, we explore the nonsingular cosmology within the framework of the Effective Field Theory (EFT) of cosmological perturbations. Due to the recently proved no-go theorem, any nonsingular cosmological models based on the cubic Galileon suffer from pathologies. We show how the EFT could help us clarify the origin of the no-go theorem, and offer us solutions to break the no-go. Particularly, we point out that the gradient instability can be removed by using some spatial derivative operators in EFT. Based on the EFT description, we obtain a realistic healthy nonsingular cosmological model, and show the perturbation spectrum can be consistent with the observations.

A covariant Lagrangian for stable nonsingular bounce

“…Recently, it has been found in refs. [8,9] that the operator R (3) δg 00 in EFT of nonsingular cosmologies is significant for the stability of bounce. Here, based on the covariant description of the R (3) δg 00 operator, we propose a covariant theory (3.1) for stable nonsingular bounce.…”

“…Our (3.1) is actually a subclass of the DHOST theory [22,23], but the cosmological background is set only by P (φ, X). The P (φ, X) nonsingular bounce model could be ghostfree [31,37], but suffers the problem of c 2 s < 0, which can not be dispelled by using the Galileon interaction ∼ φ [6][7][8][9]. Actually, in [10,38], it is observed that the Galileon interaction only moves the period of c 2 s < 0 to the outside of the bounce phase, but can not remove it, see also earlier [39].…”

“…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. It is found that the stable nonsingular cosmological models can be implemented only in the theories beyond cubic Galileon, (see also [11,12]).…”

“…[8,10]. It should be mentioned that if f 1 = 0, we have c 2 s ∼ −Ḣ < 0 around the bounce point, thus S δg 00 R (3) is needed to contribute f 1 .…”

“…[8,9], with the EFT of nonsingular cosmologies, it has been found that the operator R (3) δg 00 is significant for the stability of nonsingular bounce. Actually, in unitary gauge, without getting involved in the specific theories,…”