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

Abstract

In the model where Primordial Black Holes (PBHs) form from large primordial curvature (C) perturbations, i.e., CPBHs, constraints on PBH abundance provide in principle constraints on the primordial curvature power spectrum. This connection however depends necessarily on the details of PBH formation mechanism. In this paper we provide, for the first time, constraints on the primordial curvature power spectrum from the latest limits on PBH abundance, taking into account all the steps from gravitational collapse in real space to PBH formation. In particular, we use results from numerical relativity simulations and peak theory to study the conditions for PBH formation for a range of perturbation shapes, including nonlinearities, perturbation profile and a careful treatment of smoothing and filtering scales. We then obtain updated PBH formation conditions and translate that into primordial spectrum constraints for a wide range of shapes and abundances. These updated constraints cover a range of scales not probed by other cosmological observables. Our results show that the correct and accurate modelling of non-linearities, filtering and typical perturbation profile, is crucial for deriving meaningful cosmological implications.

Initial clustering and the primordial black hole merger rate

“…Full consideration of this will require consideration of the the shape of the small-scale power spectrum, typical profile shapes and the shape of the bispectrum, amongst other factors, and goes beyond the scope of this paper. However, much work has been completed on this topic in the past [15,[19][20][21][22][23][24][25]27], and a more complete analysis using the methods presented in this paper would yield qualitatively similar results. We have also only considered an expansion to second order in local-type non-Gaussianity, although it has been shown that higher-order terms can also be important [21].…”

Resonant backreaction in axion inflation

“…For a given amplitude of the scalar power spectrum, the probability of forming PBHs depends on the statistical properties of the scalar fluctuations, since typically PBH formation is a rare event occurring in the tail of the distribution function. For a gaussian distribution any power spectrum generating stable black holes with ζ 2 10 −2 leads to an overclosure of the universe [48]. For a positive χ 2 -distribution, as expected for the sourced scalar perturbations in axion inflation, this value is lowered to ζ 2 10 −3 [14].…”

Primordial black holes as a dark matter candidate

“…However this scale dependence is smaller than the uncertainties discussed in section 2.1, and therefore we do not include it here 12. To translate from k to M H we use equation(8), from reference[52], which agrees with the conversion given in reference[26]. However we note a discrepancy with reference[59].…”