On primordial black holes and secondary gravitational waves generated from inflation with solo/multi-bumpy potential *

Abstract

It is well known that primordial black hole (PBH) can be generated in inflation process of the early universe, especially when the inflaton field has some non-trivial features that could break the slow-roll condition. In this paper, we investigate a toy model of inflation with bumpy potential, which has one or several bumps. We found that potential with multi-bump can give rise to power spectra with multi peaks in small-scale region, which can in turn predict the generation of primordial black holes in various mass ranges. We also consider the two possibilities of PBH formation by spherical collapse and elliptical collapse. And discusses the scalar-induced gravitational waves (SIGWs) generated by the second-order scalar perturbations.

Anatomy of single-field inflationary models for primordial black holes

“…Large peaks in the power spectrum can also be induced by introducing a dump/dip 1 or a step to the potential. In the bumpy/dippy models [74,79,82,99,105,109], a small, often a Gaussian bump/dip multiplies a base potential. As bumps and dips can be placed anywhere in the potential, they can produce PBHs in a wide range of masses.…”

Ruling Out Primordial Black Hole Formation From Single-Field Inflation

“…Models with an extremely flat feature fall in this category including those with an inflection point in the potential [7,. Other examples of feature are a tiny bump or dip [61][62][63][64][65][66], an upward or downward step [67][68][69][70][71][72], polynomial shape [73][74][75][76] and Coleman-Weinberg potential [39,77,78]. In these examples, modification of potential makes a sharp η transition on the inflaton dynamics.…”

Gravitational waves from no-scale supergravity

“…We expect that this feature can be imprinted in the scalar power spectrum. On the other hand, there are many mechanisms in order to obtain an enhancement in scalar power spectrum, such as two field models, models with bumpy features [76,77]. In Appendix B there is a comparison between some models.…”

“…(3.7) and (3.8) with blue lines. Orange lines corresponds to the model presented in [77] where the enhancement of power spectrum comes from a bulky potential. Green lines to the two-model shown in [24].…”