Primordial black holes dark matter from inflection point models of inflation and the effects of reheating

Abstract

We study the generation of primordial black holes (PBH) in a single field inflection point model of inflation wherein the effective potential is expanded up to the sextic order and the inversion symmetry is imposed such that only even powers are retained in the potential. By working with a quasi-inflection point, we find that PBHs can be produced in our scenario in a very relevant mass range with a nearly monochromatic mass fraction which can account for a sizeable fraction of the cold dark matter in the universe. With changing various parameters in our model, we can also generate PBHs in a higher mass range but the primordial spectrum of curvature perturbations becomes strongly tilted at the CMB scales. We briefly discuss already existing difficulties and uncertainties associated with the computation of the PBH mass fraction for a given inflationary model. Moreover, we study the effects of a reheating epoch after the end of inflation on the PBH mass fraction and find that an epoch of a matter dominated reheating can shift the mass fraction to a larger mass range as well as increase their fractional contribution to the total dark matter even for the case of a monochromatic mass fraction.

PBH in single field inflation: the effect of shape dispersion and non-Gaussianities

“…Perturbations with ζ g > µ * are so large that they prevent the inflaton field from overshooting the local maximum [25]. The regions where the inflaton is trapped in the false vacuum are localized false vacuum bubbles which, from the spectrum, but if the distribution is non-Gaussian, the shape will also depend on the nature of the non-Gaussianity [23,41,42]. Furthermore, since fluctuations are drawn from a statistical distribution, the shapes of perturbations susceptible of collapsing will inherit a dispersion.…”

“…While the mean profile is usually taken to be representative of the typical shape, it seems important to consider how the threshold may vary due to the dispersion of shapes. This point is particularly relevant when a mean profile for the perturbations cannot be defined, as it is the case for large overdensities coming from the model of single-field inflation with a barrier 4 [23].…”

“…In order to make accurate predictions on the statistical properties of PBHs, it is necessary to be specific about their formation process. One of the simplest mechanisms is the collapse of large adiabatic perturbations seeded during a period of single-field inflation [14][15][16][17][18][19][20][21][22][23]. While fluctuations must be predominantly Gaussian at the cosmic microwave background scales, those leading to PBH formation at smaller scales are typically non-Gaussian [24-27] 2 .…”

Initial clustering and the primordial black hole merger rate

“…The term In order to derive a mass function, we will, again, make the simplifying assumption that all PBH formation occurs at a single epoch, with a Dirac-delta form for the power spectrum, as in equation (17). It is noted that such a form for the power spectrum is not physical, and the fastest growth for the power spectrum as a function of the wavevector k has been shown to be ∼ k 4 [64], or slightly steeper in the case of a more contrived scenario [65] (see also [66]), which means that PBH formation at a single scale is not physical, but rather that it occurs over a range of scales.…”

From primordial black holes abundance to primordial curvature power spectrum (and back)

“…In particular, there are a plethora of inflationary scenarios able to generate PBHs in the late Universe, see e.g., Refs. [80][81][82][83][84][85][86][87][88][89][90][91][92][93]. In this paper we concentrate on this scenario of PBHs generated by primordial curvature (C) perturbations, CPBHs.…”