A novel formulation of the PBH mass function
arXiv:1912.04687
Abstract
Computations of the primordial black hole (PBH) mass function discussed in the literature have conceptual issues. They stem from that the mass function is a differential quantity and the standard criterion of the PBH formation from the seed primordial fluctuations cannot be directly applied to the computation of the differential quantities. We propose a new criterion of the PBH formation which is an addition of one extra condition to the existing one. By doing this, we derive a formal expression of the PBH mass function without introducing any ambiguous interpretations which exist in the previous studies. Once the underlying primordial fluctuations are specified, the PBH mass function can be in principle determined by the new formula. As a demonstration of our formulation, we compute the PBH mass function analytically for the case where the perturbations are Gaussian and the space is one dimension.
arXiv comment11 pages, 1 figure
References in corpus (21)
- New cosmological constraints on primordial black holes
- Primordial Black Holes as Dark Matter
- Primordial black hole constraints for extended mass functions
- Threshold of primordial black hole formation
- Near-Critical Gravitational Collapse and the Initial Mass Function of Primordial Black Holes
- Dynamics of Primordial Black Hole Formation
- Black hole formation in the Friedmann universe: Formulation and computation in numerical relativity
- Steepest growth of the power spectrum and primordial black holes
- Threshold for primordial black holes: Dependence on the shape of the cosmological perturbations
- The abundance of primordial black holes depends on the shape of the inflationary power spectrum
- Inflationary Primordial Black Holes as All Dark Matter
- A universal threshold for primordial black hole formation
- Primordial black holes with an accurate QCD equation of state
- A new calculation of the mass fraction of primordial black holes
- The Initial Spin Probability Distribution of Primordial Black Holes
- Cosmological constraints on primordial black holes produced in the near-critical gravitational collapse
- Effect of nonlinearity between density and curvature perturbations on the primordial black hole formation
- Constraints on amplitudes of curvature perturbations from primordial black holes
- Primordial Black Holes: Do They Exist and Are They Useful?
- Constraints on the primordial curvature perturbation from primordial black holes
- Formation threshold of rotating primordial black holes
Cited by in corpus (5)
- The First Three Seconds: a Review of Possible Expansion Histories of the Early Universe
- Solar-Mass Primordial Black Holes Explain NANOGrav Hint of Gravitational Waves
- Non-linear statistics of primordial black holes from gaussian curvature perturbations
- Primordial black holes from metric preheating: mass fraction in the excursion-set approach
- Baryogenesis from ultra-slow-roll inflation