  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.
