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Paper IPM / Astronomy / 17453  


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 nonperturbative Ã?ÃÂ´N formalism as a method to nonperturbatively 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 nonattractor singlefield 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 powerlaw tail, a doubleexponential tail, and a doubly peaked distribution can all be realized for the curvature perturbation in the singlefield nonattractor models of inflation. We thus show that there is a diverse zoo of possible tails from inflation so that a modeldependent, nonperturbative study of the distribution of the primordial fluctuations seems inevitable concerning PBH abundance
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