# A Tail of Eternal Inflation

### Submission summary

 Authors (as Contributors): Timothy Cohen
Submission information
Date submitted: 2022-10-12 09:46
Submitted by: Cohen, Timothy
Submitted to: SciPost Physics
Ontological classification
Specialties:
• Gravitation, Cosmology and Astroparticle Physics
• High-Energy Physics - Theory
Approach: Theoretical

### Abstract

Non-trivial inflaton self-interactions can yield calculable signatures of primordial non-Gaussianity that are measurable in cosmic surveys. We calculate the non-Gaussian corrections to Stochastic Inflation within the framework of Soft de Sitter Effective Theory, from which we derive the associated probability distribution for the scalar fluctuations. As a consequence of this new result, we show that the phase transition to slow-roll eternal inflation is often incalculable in these models. Instead, this transition is sensitive to the non-Gaussian tail of the distribution of scalar fluctuations, which probes physics inside the horizon, potentially beyond the cutoff scale of the Effective Field Theory of Inflation. We delineate the parameter space consistent with current observations and weak coupling at horizon crossing in which the large fluctuations relevant for eternal inflation can only be determined by appealing to a UV completion. We also argue that this breakdown of the perturbative description is required for the de Sitter entropy to reflect the number of de Sitter microstates.

###### Current status:
Voting in preparation

### Author comments upon resubmission

Dear Editor,

We appreciate that the referees both disagree with our expectations for when the EFTs used to derive the formalism of Stochastic Inflation for the inflaton should break down. Given that there are no objections to the novel technical results in our paper, we have edited the paper to eliminate any subjective discussion. We have now focused the message of the paper on the concrete technical results and the way in which they can be used to demonstrate a quantitative issue with the validity of the EFT.

We hope that given this change in tone, the referees will now agree that our paper is suitable for publication in SciPost.

### List of changes

We made substantial wording changes to the abstract, introduction, and conclusions to change the tone as discussed in the response. The equations and figures are unchanged.

### Submission & Refereeing History

Resubmission scipost_202210_00062v1 on 12 October 2022
Submission 2111.09332v2 on 8 July 2022

## Reports on this Submission

### Report

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.

• validity: good
• significance: high
• originality: high
• clarity: high
• formatting: excellent
• grammar: excellent

### Report

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

• validity: -
• significance: -
• originality: -
• clarity: -
• formatting: -
• grammar: -