Volume 142, Number 4, May 2023
|Number of page(s)||7|
|Section||Gravitation, cosmology and astrophysics|
|Published online||30 May 2023|
Non-perturbative non-Gaussianity and primordial black holes
1 Institute of Cosmology & Gravitation, University of Portsmouth - Dennis Sciama Building, Burnaby Road, Portsmouth, PO1 3FX, UK
2 School of Mathematics and Physics, University of Portsmouth - Lion Gate Building, Lion Terrace, Portsmouth, PO1 3HF, UK
3 Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, CNRS, Université PSL, Sorbonne Université, Université Paris Cité - 75005 Paris, France
4 Laboratoire Astroparticule et Cosmologie, CNRS, Université Paris Cité - 75013 Paris, France
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Received: 25 January 2023
Accepted: 10 May 2023
We present a non-perturbative method for calculating the abundance of primordial black holes given an arbitrary one-point probability distribution function for the primordial curvature perturbation, . A non-perturbative method is essential when considering non-Gaussianities that cannot be treated using a conventional perturbative expansion. To determine the full statistics of the density field, we relate ζ to a Gaussian field by equating the cumulative distribution functions. We consider two examples: a specific local-type non-Gaussian distribution arising from ultra slow roll models, and a general piecewise model for with an exponential tail. We demonstrate that the enhancement of primordial black hole formation is due to the intermediate regime, rather than the far tail. We also show that non-Gaussianity can have a significant impact on the shape of the primordial black hole mass distribution.
© 2023 The author(s)
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