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We update the constraints on the fraction of the Universe that may have gone into primordial black holes (PBHs) over the mass range $10^{-5}text{--}10^{50}$ g. Those smaller than $sim 10^{15}$ g would have evaporated by now due to Hawking radiation, so their abundance at formation is constrained by the effects of evaporated particles on big bang nucleosynthesis, the cosmic microwave background (CMB), the Galactic and extragalactic $gamma$-ray and cosmic ray backgrounds and the possible generation of stable Planck mass relics. PBHs larger than $sim 10^{15}$ g are subject to a variety of constraints associated with gravitational lensing, dynamical effects, influence on large-scale structure, accretion and gravitational waves. We discuss the constraints on both the initial collapse fraction and the current fraction of the CDM in PBHs at each mass scale but stress that many of the constraints are associated with observational or theoretical uncertainties. We also consider indirect constraints associated with the amplitude of the primordial density fluctuations, such as second-order tensor perturbations and $mu$-distortions arising from the effect of acoustic reheating on the CMB, if PBHs are created from the high-$sigma$ peaks of nearly Gaussian fluctuations. Finally we discuss how the constraints are modified if the PBHs have an extended mass function, this being relevant if PBHs provide some combination of the dark matter, the LIGO/Virgo coalescences and the seeds for cosmic structure. Even if PBHs make a small contribution to the dark matter, they could play an important cosmological role and provide a unique probe of the early Universe.
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The fraction of the Universe going into primordial black holes (PBHs) with initial mass M_* approx 5 times 10^{14} g, such that they are evaporating at the present epoch, is strongly constrained by observations of both the extragalactic and Galactic gamma-ray backgrounds. However, while the dominant contribution to the extragalactic background comes from the time-integrated emission of PBHs with initial mass M_*, the Galactic background is dominated by the instantaneous emission of those with initial mass slightly larger than M_* and current mass below M_*. Also, the instantaneous emission of PBHs smaller than 0.4 M_* mostly comprises secondary particles produced by the decay of directly emitted quark and gluon jets. These points were missed in the earlier analysis by Lehoucq et al. using EGRET data. For a monochromatic PBH mass function, with initial mass (1+mu) M_* and mu << 1, the current mass is (3mu)^{1/3} M_* and the Galactic background constrains the fraction of the Universe going into PBHs as a function of mu. However, the initial mass function cannot be precisely monochromatic and even a tiny spread of mass around M_* would generate a current low-mass tail of PBHs below M_*. This tail would be the main contributor to the Galactic background, so we consider its form and the associated constraints for a variety of scenarios with both extended and nearly-monochromatic initial mass functions. In particular, we consider a scenario in which the PBHs form from critical collapse and have a mass function which peaks well above M_*. In this case, the largest PBHs could provide the dark matter without the M_* ones exceeding the gamma-ray background limits.
The detection of binary black hole coalescences by LIGO/Virgo has aroused the interest in primordial black holes (PBHs), because they could be both the progenitors of these black holes and a compelling candidate of dark matter (DM). PBHs are formed soon after the enhanced scalar perturbations re-enter horizon during radiation dominated era, which would inevitably induce gravitational waves as well. Searching for such scalar induced gravitational waves (SIGWs) provides an elegant way to probe PBHs. We perform the first direct search for the signals of SIGWs accompanying the formation of PBHs in North American Nanohertz Observatory for Gravitational waves (NANOGrav) 11-year data set. No statistically significant detection has been made, and hence we place a stringent upper limit on the abundance of PBHs at $95%$ confidence level. In particular, less than one part in a million of the total DM mass could come from PBHs in the mass range of $[2 times 10^{-3}, 7times 10^{-1}] Msun$.
Evidences for the primordial black holes (PBH) presence in the early Universe renew permanently. New limits on their mass spectrum challenge existing models of PBH formation. One of the known model is based on the closed walls collapse after the inflationary epoch. Its intrinsic feature is multiple production of small mass PBH which might contradict observations in the nearest future. We show that the mechanism of walls collapse can be applied to produce substantially different PBH mass spectra if one takes into account the classical motion of scalar fields together with their quantum fluctuations at the inflationary stage.
Primordial black holes (PBHs) are of fundamental interest in cosmology and astrophysics, and have received much attention as a dark matter candidate and as a potential source of gravitational waves. One possible PBH formation mechanism is the gravitational collapse of cosmic strings. Thus far, the entirety of the literature on PBH production from cosmic strings has focused on the collapse of (quasi)circular cosmic string loops, which make up only a tiny fraction of the cosmic loop population. We demonstrate here a novel PBH formation mechanism: the collapse of a small segment of cosmic string in the neighbourhood of a cusp. Using the hoop conjecture, we show that collapse is inevitable whenever a cusp appears on a macroscopically-large loop, forming a PBH whose rest mass is smaller than the mass of the loop by a factor of the dimensionless string tension squared, $(Gmu)^2$. Since cusps are generic features of cosmic string loops, and do not rely on finely-tuned loop configurations like circular collapse, this implies that cosmic strings produce PBHs in far greater numbers than has previously been recognised. The resulting PBHs are highly spinning and boosted to ultrarelativistic velocities; they populate a unique region of the BH mass-spin parameter space, and are therefore a smoking gun observational signature of cosmic strings. We derive new constraints on $Gmu$ from the evaporation of cusp-collapse PBHs, and update existing constraints on $Gmu$ from gravitational-wave searches.
The renewed interest in the possibility that primordial black holes (PBHs) may constitute a significant part of the dark matter has motivated revisiting old observational constraints, as well as developing new ones. We present new limits on the PBH abundance, from a comprehensive analysis of high-resolution, high-redshift Lyman-$alpha$ forest data. Poisson fluctuations in the PBH number density induce a small-scale power enhancement which departs from the standard cold dark matter prediction. Using a grid of hydrodynamic simulations exploring different values of astrophysical parameters, {we obtain a marginalized upper limit on the PBH mass of $f_{rm PBH}M_{rm PBH} sim 60~M_{odot}$ at $2sigma$, when a Gaussian prior on the reionization redshift is imposed, preventing its posterior distribution to peak on very high values, which are disfavoured by the most recent estimates obtained both through Cosmic Microwave Background and Inter-Galactic Medium observations. Such bound weakens to $f_{rm PBH}M_{rm PBH} sim 170~M_{odot}$, when a conservative flat prior is instead assumed. Both limits significantly improves previous constraints from the same physical observable.} We also extend our predictions to non-monochromatic PBH mass distributions, ruling out large regions of the parameter space for some of the most viable PBH extended mass functions.
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