A Tail of Eternal Inflation

In this paper, the authors have studied the transition to eternal inflation within the framework of stochastic inflation, importantly with the inclusion of non-Gaussianity (denoted via $f^{eq}_{NL}$ ). Particularly, they have considered a parameter regime where the scale of EFT of inflation ($\Lambda$) lies below the scale set by the breaking of time translational symmetry ($f_\pi$), i.e., $\Lambda<f_\pi$. Although the theory is still weakly coupled since the Hubble scale ($H$) lies below $\Lambda$. By looking at the tail of the scalar distribution function, they argued the breaking of stochastic inflation (while one tries to calculate the onset of eternal inflation) and tried to make it distinct from the breakdown of perturbative calculation or sensitiveness to UV physics (hinted naively by $\Lambda<f_\pi$). In my understanding, they have performed technical calculations in the paper's main text concerning non-Gaussian corrections to stochastic inflation. From their results, they have put forward the above-mentioned "interpretation". Their technical result may instigate further explorations looking into the novelty of their interpretations. Additionally, keeping in mind their revision in the abstract and introduction, in my opinion, this should be recorded in the literature and hence would recommend for its publication.

A minor typo that came to my notice: In the caption of figure 2 (the sixth line) `external inflation' should be changed to eternal inflation.

The authors have successfully addressed my previous comment. The revised manuscript is suitable for publication in SciPost Physics.