The power spectrum on small scales: Robust constraints and comparing PBH methodologies

TL;DR

This paper compares different methodologies for constraining primordial black hole formation from the power spectrum, showing that constraints are consistent across methods and aligning with pulsar timing array data, while also highlighting the impact of various physical effects.

Contribution

It provides a robust comparison of PBH constraint methods, incorporating critical collapse effects and non-linear relations, and demonstrates their consistency and implications for black hole observations.

Findings

Constraints vary by only ~10% across methods with consistent treatment.

PBH constraints align with PTA data on black hole masses.

μ-distortion constraints challenge SMBH formation and lighter PBH ranges.

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 $\sim$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 $\zeta$ and $\delta$, 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 the LIGO and Virgo, but that the $\mu$-distortion constraints rule out supermassive black hole (SMBH) formation and potentially even the much lighter mass range of $\sim$(1-100) $\mathrm{M}_\odot$ that LIGO/Virgo probes.