Infrared Logarithms in Minisuperspace Inflation

We examine the emergence of the infrared logarithms in the cosmological perturbation theory applied to the minisuperspace scalar slow-roll inflation. Not surprisingly, in the single scalar field model the curvature perturbation $\zeta$ is conserved and no $\ln a_B$ behavior appears, where $a_B(t)$ is the background scale factor of the universe. On the other hand, in the presence of a spectator scalar the $n$’th order perturbation theory gives an $(\ln a_B{)}^n$ correction to $\zeta$. However, a nonperturbative estimate shows that $\zeta$ actually becomes the sum of a constant and a mildly evolving $\ln a_B$ pieces.