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Title: Non-Gaussian fluctuations and primordial black holes from inflation

Abstract

We explore the role of non-Gaussian fluctuations in primordial black hole (PBH) formation and show that the standard Gaussian assumption, used in all PBH formation papers to date, is not justified. Since large spikes in power are usually associated with flat regions of the inflaton potential, quantum fluctuations become more important in the field dynamics, leading to mode-mode coupling and non-Gaussian statistics. Moreover, PBH production requires several {sigma} (rare) fluctuations in order to prevent premature matter dominance of the universe, so we are necessarily concerned with distribution tails, where any intrinsic skewness will be especially important. We quantify this argument by using the stochastic slow-roll equation and a relatively simple analytic method to obtain the final distribution of fluctuations. We work out several examples with toy models that produce PBH{close_quote}s, and test the results with numerical simulations. Our examples show that the naive Gaussian assumption can result in errors of many orders of magnitude. For models with spikes in power, our calculations give sharp cutoffs in the probability of large positive fluctuations, meaning that Gaussian distributions would vastly overproduce PBH{close_quote}s. The standard results that link inflation-produced power spectra and PBH number densities must then be reconsidered, since they rely quitemore » heavily on the Gaussian assumption. We point out that since the probability distributions depend strongly on the nature of the potential, it is impossible to obtain results for general models. However, calculating the distribution of fluctuations for any specific model seems to be relatively straightforward, at least in the single inflaton case. {copyright} {ital 1997} {ital The American Physical Society}« less

Authors:
;  [1]
  1. Board of Studies in Physics, University of California, Santa Cruz, California 95064 (United States)
Publication Date:
OSTI Identifier:
530243
Resource Type:
Journal Article
Journal Name:
Physical Review, D
Additional Journal Information:
Journal Volume: 55; Journal Issue: 12; Other Information: PBD: Jun 1997
Country of Publication:
United States
Language:
English
Subject:
66 PHYSICS; BLACK HOLES; FLUCTUATIONS; COSMOLOGY; STOCHASTIC PROCESSES; NUMERICAL ANALYSIS; INFLATION; DISTRIBUTION; SIMULATION; PROBABILITY

Citation Formats

Bullock, J S, and Primack, J R. Non-Gaussian fluctuations and primordial black holes from inflation. United States: N. p., 1997. Web. doi:10.1103/PhysRevD.55.7423.
Bullock, J S, & Primack, J R. Non-Gaussian fluctuations and primordial black holes from inflation. United States. https://doi.org/10.1103/PhysRevD.55.7423
Bullock, J S, and Primack, J R. 1997. "Non-Gaussian fluctuations and primordial black holes from inflation". United States. https://doi.org/10.1103/PhysRevD.55.7423.
@article{osti_530243,
title = {Non-Gaussian fluctuations and primordial black holes from inflation},
author = {Bullock, J S and Primack, J R},
abstractNote = {We explore the role of non-Gaussian fluctuations in primordial black hole (PBH) formation and show that the standard Gaussian assumption, used in all PBH formation papers to date, is not justified. Since large spikes in power are usually associated with flat regions of the inflaton potential, quantum fluctuations become more important in the field dynamics, leading to mode-mode coupling and non-Gaussian statistics. Moreover, PBH production requires several {sigma} (rare) fluctuations in order to prevent premature matter dominance of the universe, so we are necessarily concerned with distribution tails, where any intrinsic skewness will be especially important. We quantify this argument by using the stochastic slow-roll equation and a relatively simple analytic method to obtain the final distribution of fluctuations. We work out several examples with toy models that produce PBH{close_quote}s, and test the results with numerical simulations. Our examples show that the naive Gaussian assumption can result in errors of many orders of magnitude. For models with spikes in power, our calculations give sharp cutoffs in the probability of large positive fluctuations, meaning that Gaussian distributions would vastly overproduce PBH{close_quote}s. The standard results that link inflation-produced power spectra and PBH number densities must then be reconsidered, since they rely quite heavily on the Gaussian assumption. We point out that since the probability distributions depend strongly on the nature of the potential, it is impossible to obtain results for general models. However, calculating the distribution of fluctuations for any specific model seems to be relatively straightforward, at least in the single inflaton case. {copyright} {ital 1997} {ital The American Physical Society}},
doi = {10.1103/PhysRevD.55.7423},
url = {https://www.osti.gov/biblio/530243}, journal = {Physical Review, D},
number = 12,
volume = 55,
place = {United States},
year = {Sun Jun 01 00:00:00 EDT 1997},
month = {Sun Jun 01 00:00:00 EDT 1997}
}