Abstract
We compare primordial black hole (PBH) constraints on the power spectrum and mass distributions using the traditional Press Schechter formalism, peaks theory, and a recently developed version of peaks theory relevant to PBHs. We show that, provided the PBH formation criteria and the power spectrum smoothing are treated consistently, the constraints only vary by ∼ 10% between methods (a difference that will become increasingly important with better data). Our robust constraints from PBHs take into account the effects of critical collapse, the non-linear relation between ζ and δ, and the shift from the PBH mass to the power spectrum peak scale. We show that these constraints are remarkably similar to the pulsar timing array (PTA) constraints impacting the black hole masses detected by LIGO and Virgo, but that the μ-distortion constraints rule out supermassive black hole (SMBH) formation and potentially even the much lighter mass range of ∼(1–100) M☉ that LIGO/Virgo probes.
Highlights
We compare primordial black hole (PBH) constraints on the power spectrum and mass distributions using the traditional Press Schechter formalism, peaks theory, and a recently developed version of peaks theory relevant to PBHs
Tight constraints on fPBH for MPBH 10−6 M are possible if the majority of dark matter consists of “standard” WIMPs [4, 96,97,98,99,100]. We show these constraints in fig. 6, as well as future μ-distortion constraints from a detector like the Primordial Inflation Explorer (PIXIE) [101], and future gravitational wave background constraints from the Square Kilometre Array (SKA), the Laser Interferometer Space Antenna (LISA), and the Einstein Telescope (ET)5
We have made the first detailed analysis of how the PBH mass distribution shape and amplitude varies between three different techniques to calculate the primordial mass distribution: Press Schechter, traditional peaks theory and a newly developed peaks theory variation
Summary
The procedure for obtaining the mass distribution from the power spectrum is similar for all three methods considered, and is based on connecting the PBH abundance ΩPBH to the mass fraction β. The width ∆ is a free parameter, and we will normally choose two representative values for the width, ∆ = 0.3 as a narrow peak which results in a PBH mass distribution not very different from that due to a delta-function power spectrum, and ∆ = 1 as a broad peak which is roughly what one would expect if the inflaton field dynamics change over a time-scale of 1-efolding during inflation.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
