Extreme scenarios: the tightest possible constraints on the power spectrum due to primordial black holes

Abstract

Observational constraints on the abundance of primordial black holes (PBHs) constrain the allowed amplitude of the primordial power spectrum on both the smallest and the largest ranges of scales, covering over 20 decades from $1-10^{20}/\mathrm{Mpc}$. Despite tight constraints on the allowed fraction of PBHs at their time of formation near horizon entry in the early universe, the corresponding constraints on the primordial power spectrum are quite weak, typically ${\mathcal{P}}_{\mathcal{R}}\lesssim 10^{-2}$ assuming Gaussian perturbations. Motivated by recent claims that the evaporation of just one PBH would destabilise the Higgs vacuum and collapse the universe, we calculate the constraints which follow from assuming there are zero PBHs within the observable universe. This extends the constraints right down to the horizon scale at the end of inflation, but does not significantly tighten the existing power spectrum constraints, even though the constraint on PBH abundance can decrease by up to 46 orders of magnitude. This shows that no future improvement in observational constraints can ever lead to a significant tightening in constraints on inflation (via the power spectrum amplitude). The power spectrum constraints are weak because an order unity perturbation is required in order to overcome pressure forces. We therefore consider an early matter dominated era, during which exponentially more PBHs form for the same initial conditions. We show this leads to far tighter constraints, which approach ${\mathcal{P}}_{\mathcal{R}}\lesssim 10^{-9}$, albeit over a smaller range of scales and are very sensitive to when the early matter dominated era ends. Finally, we show that an extended early matter era is incompatible with the argument that an evaporating PBH would destroy the universe, unless the power spectrum amplitude decreases by up to ten orders of magnitude.

16 pages, 5 figures. Minor clarifications and references added, matches published version

References in corpus (14)

• Limits on the Macho Content of the Galactic Halo from the EROS-2 Survey of the Magellanic Clouds
• Primordial black holes from single field models of inflation
• Cosmic microwave background limits on accreting primordial black holes
• Primordial black hole constraints for extended mass functions
• Inflationary Primordial Black Holes as All Dark Matter
• Generalised constraints on the curvature perturbation from primordial black holes
• The end of the MACHO era- revisited: new limits on MACHO masses from halo wide binaries
• Massive Primordial Black Holes as Dark Matter and their detection with Gravitational Waves
• Dynamics of dwarf galaxies disfavor stellar-mass black hole dark matter
• Constraints on Primordial Black Holes with Extended Mass Functions
• Primordial black holes from inflaton and spectator field perturbations in a matter-dominated era
• Probing Primordial-Black-Hole Dark Matter with Gravitational Waves
• A Preferred Mass Range for Primordial Black Hole Formation and Black Holes as Dark Matter Revisited
• The long-short wavelength mode coupling tightens primordial black hole constraints

Cited by in corpus (27)

• Fundamental Physics with the Square Kilometre Array
• Steepest growth of the power spectrum and primordial black holes
• Dissecting the growth of the power spectrum for primordial black holes
• From Primordial Black Holes Abundance to Primordial Curvature Power Spectrum (and back)
• Questions on calculation of primordial power spectrum with large spikes: the resonance model case
• EFT Compatible PBHs: Effective Spawning of the Seeds for Primordial Black Holes during Inflation
• Constraints on the primordial curvature power spectrum from primordial black holes
• Small-scale structure of primordial black hole dark matter and its implications for accretion
• Primordial black holes from single-field inflation: a fine-tuning audit
• Phenomenology of Self-Interacting Dark Matter in a Matter-Dominated Universe
• Primordial Black Hole Formation During Slow Reheating After Inflation
• Non-Gaussianity in inflationary scenarios for primordial black holes
• Electroweak Vacuum Collapse induced by Vacuum Fluctuations of the Higgs Field around Evaporating Black Holes
• Gravitational waves $\times$ HI intensity mapping: cosmological and astrophysical applications
• Constraints on the curvature power spectrum from primordial black hole evaporation
• Light Primordial Exotic Compact Objects as All Dark Matter
• Window function dependence of the novel mass function of primordial black holes
• The effect of outflows on CMB bounds from Primordial Black Hole accretion
• Small-scale primordial fluctuations in the 21cm Dark Ages signal
• Impact of Primordial Black Hole Dark Matter on Gas Properties at Very High Redshift: A Semi-Analytical Model
• Primordial Black Holes in the Excursion Set Theory
• Primordial Black Holes from Pre-Big Bang inflation
• Is the formation of primordial black holes from single-field inflation compatible with standard cosmology?
• Robust μ-distortion constraints on primordial supermassive black holes from cubic (gNL) non-Gaussian perturbations
• Constraints on primordial black holes for nonstandard cosmologies
• Enhanced Small-Scale Structure in the Cosmic Dark Ages
• Impact of facility timing and coordination for next-generation gravitational-wave detectors