Primordial black holes from polynomial potentials in single field inflation
Abstract
Within canonical single field inflation models, we provide a method to reverse engineer and reconstruct the inflaton potential from a given power spectrum. This is not only a useful tool to find a potential from observational constraints, but also gives insight into how to generate a large amplitude spike in density perturbations, especially those that may lead to primordial black holes (PBHs). In accord with other works, we find that the usual slowroll conditions need to be violated in order to generate a significant spike in the spectrum. We find that a way to achieve a very large amplitude spike in single field models is for the classical roll of the inflaton to overshoot a local minimum during inflation. We provide an example of a quintic polynomial potential that implements this idea and leads to the observed spectral index, observed amplitude of fluctuations on large scales, significant PBH formation on small scales, and is compatible with other observational constraints. We quantify how much finetuning is required to achieve this in a family of random polynomial potentials, which may be useful to estimate the probability of PBH formation in the string landscape.
 Publication:

Physical Review D
 Pub Date:
 April 2018
 DOI:
 10.1103/PhysRevD.97.083509
 arXiv:
 arXiv:1712.09750
 Bibcode:
 2018PhRvD..97h3509H
 Keywords:

 Astrophysics  Cosmology and Nongalactic Astrophysics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Phenomenology;
 High Energy Physics  Theory
 EPrint:
 13 pages in double column format, 5 figures. V2: Added references and small clarifications