Is asymptotically safe inflation eternal?

TL;DR

This paper investigates whether eternal inflation is compatible with the asymptotic safety approach to quantum gravity, finding no inherent contradiction and suggesting eternal inflation cannot occur within the effective field theory regime.

Contribution

It explores the relationship between eternal inflation and asymptotic safety, analyzing specific inflationary models and RG-improved actions to establish their compatibility.

Findings

No tension between eternal inflation and asymptotic safety in matter and gravitational sectors.

Eternal inflation cannot occur within the effective field theory range of quantum gravity.

Analytical and numerical analysis supports the constraints on eternal inflation models.

Abstract

Recently, based on swampland considerations in string theory, the (no) eternal inflation principle has been put forward. The natural question arises whether similar conditions hold in other approaches to quantum gravity. In this article, the asymptotic safety hypothesis is considered in the context of eternal inflation. As exemplary inflationary models the SU(N) Yang-Mills in the Veneziano limit and various RG-improvements of the gravitational action are studied. The existence of UV fixed point generically flattens the potential and our findings suggest no tension between eternal inflation and asymptotic safety, both in the matter and gravitational sector in contradistinction to string theory. Moreover, the eternal inflation cannot take place in the range of applicability of effective field quantum gravity theory. We employ the analytical relations for eternal inflation to some of the models with single minima, such as Starobinsky inflation, alpha-attractors, or the RG-improved models and verify them with the massive numerical simulations. The validity of these constraints is also discussed for a multi-minima model.