Tail diversity from inflation

TL;DR

This paper investigates the diverse possible tail behaviors of primordial fluctuation distributions in inflationary models, highlighting the limitations of Gaussian assumptions and emphasizing the need for non-perturbative methods to accurately estimate primordial black hole abundance.

Contribution

It introduces a non-perturbative $ abla$ formalism for estimating the PDF of primordial fluctuations and demonstrates the variety of tail behaviors in single-field inflation models affecting PBH predictions.

Findings

Gaussian extrapolation can drastically underestimate large fluctuation likelihood.

Various tail types like power-law and double-exponential can occur in inflation models.

Non-perturbative analysis is essential for accurate PBH abundance estimates.

Abstract

The tail of the distribution of primordial fluctuations (corresponding to the likelihood of realization of large fluctuations) is of interest, from both theoretical and observational perspectives. In particular, it is relevant for the accurate evaluation of the primordial black hole (PBH) abundance. In this paper, we first analyze the non-perturbative $\delta N$ formalism as a method to non-perturbatively estimate the probability distribution function (PDF) of primordial fluctuations, discuss its underlying assumptions and deal with several subtleties that may arise as a result of considering large fluctuations. Next, we employ the method to study several non-attractor single-field inflationary models as the simplest examples that may lead to the abundant production of PBHs. We conclude that the Gaussian extrapolation from linear perturbation theory may fail drastically to predict the likelihood of large fluctuations. Specifically, we show that a truncation of the tail, a power-law tail, a double-exponential tail, and a doubly peaked distribution can all be realized for the curvature perturbation in the single-field non-attractor models of inflation. We thus show that there is a diverse zoo of possible tails from inflation so that a model-dependent, non-perturbative study of the distribution of the primordial fluctuations seems inevitable concerning PBH abundance.