Cosmic conundra explained by thermal history and primordial black holes

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Abstract

A universal mechanism may be responsible for several unresolved cosmic conundra. The sudden drop in the pressure of relativistic matter at W±Z0 decoupling, the quark–hadron transition and e+e annihilation enhances the probability of primordial black hole (PBH) formation in the early Universe. Assuming the amplitude of the primordial curvature fluctuations is approximately scale-invariant, this implies a multi-modal PBH mass spectrum with peaks at 106, 1, 30, and 106M. This suggests a unified PBH scenario which naturally explains the dark matter and recent microlensing observations, the LIGO/Virgo black hole mergers, the correlations in the cosmic infrared and X-ray backgrounds, and the origin of the supermassive black holes in galactic nuclei at high redshift. A distinctive prediction of our model is that LIGO/Virgo should observe black hole mergers in the mass gaps between 2 and 5M (where no stellar remnants are expected) and above 65M (where pair-instability supernovae occur) and low-mass-ratios in between. Therefore the recent detection of events GW190425, GW190814 and GW190521 with these features is striking confirmation of our prediction and may indicate a primordial origin for the black holes. In this case, the exponential sensitivity of the PBH abundance to the equation of state would offer a unique probe of the QCD phase transition. The detection of PBHs would also offer a novel way to probe the existence of new particles or phase transitions with energy between 1MeV and 1010  GeV.

Introduction

Primordial black holes (PBHs) in the solar-mass range have attracted a lot of attention since the LIGO/Virgo detection of gravitational waves from coalescing black holes [1]. The observed merger rate is compatible with what would be expected if PBHs constitute an appreciable fraction, and possibly all, of the cold dark matter (CDM). Moreover, the LIGO/Virgo observations seem to favour mergers with low effective spins, as expected for PBHs but hard to explain for black holes of stellar origin [2]. An extended PBH mass function with a peak in the range 110M could explain the LIGO/Virgo observations. Based on an argument related to gravitational lensing by PBH clusters, we show that the usual dark-matter constraints from the microlensing of stars, supernovae and quasars in this range can be evaded.

Given the revival of interest in PBHs, one must explain why they have the mass and density required for explaining the LIGO/Virgo events, and why these values are comparable to the mass and density of stars. One approach is to choose an inflationary scenario which produces a peak in the power spectrum of curvature fluctuations at the appropriate scale [3]. The required amplitude of the inhomogeneities must be much larger than that observed on cosmological scales but not too large, so this requires fine-tuning of both the scale and amplitude.

An alternative approach is to assume the power spectrum is smooth (i.e. featureless) but that there is a sudden change in the plasma pressure at a particular cosmological epoch, allowing PBHs to form more easily then. Enhanced gravitational collapse occurs because the critical density fluctuation required for PBH formation (δc) decreases when the equation-of-state parameter (wpρc2) is reduced. Since the PBH collapse fraction depends exponentially on δc for Gaussian fluctuations [4], this can have a strong effect on the fraction of CDM in PBHs. This is particularly important for the Quantum Chromodynamics (QCD) transition at 105s, lattice-gauge-theory calculations indicating that the sound-speed decreases by around 30% then [5], [6], [7], [8], [9], [10], [11].

PBHs formed at the QCD transition would naturally have the Chandrasekhar mass (1.4M), this also characterising the mass of main-sequence stars, and a collapse fraction of order the cosmic baryon-to-photon ratio (109) if PBHs provide most of the dark matter [12]. The latter feature is naturally explained if PBH formation generates a hot outgoing shower of relativistic particles because electroweak baryogenesis can occur very efficiently there and produce a local baryon-to-photon ratio of order unity [13].

In this paper we point out an interesting consequence of the above scenario, by extending it beyond the QCD scale. As the background temperature decreases from 100  GeV to 1  MeV, corresponding to the rest masses of the W and Z bosons, the proton, the pion and the electron, there are four periods at which the sound speed exhibits sudden dips. The proton dip is the biggest (30%) but the others can also be significant (5–10%) because of the exponential dependence of the gravitational collapse probability on the critical curvature fluctuation. These dips produce distinctive features in the PBH mass function at four mass scales in the range 10−6106M.

An important feature of this scenario is that it predicts the form of the PBH mass distribution very precisely. We show that for a nearly scale-invariant primordial power spectrum, the expected form not only satisfies all the current astrophysical and cosmological constraints, but also allows the PBHs to explain numerous observational conundra: (1) microlensing events towards the Galactic bulge generated by planet-mass objects with about 1% of the CDM density [14], well above most expectations for free-floating planets; (2) microlensing of quasars [15], including ones that are so misaligned with the lensing galaxy that the probability of lensing by a star is very low; (3) the unexpected high number of microlensing events towards the Galactic bulge by dark objects in the mass gap between 2 and 5M [16], where stellar evolution models fail to form black holes [17]; (4) unexplained correlations in the source-subtracted X-ray and cosmic infrared background fluctuations [18]; (5) the non-observation of ultra-faint dwarf galaxies below the critical radius of dynamical heating by PBHs [19]; (6) the masses, spins and coalescence rates for the black holes found by LIGO/Virgo [20], including two recent events with black holes which are probably in the mass gap; (7) the relationship between the mass of a galaxy and that of its central black hole.

Section snippets

Thermal history of the universe

Reheating at the end of inflation fills the Universe with radiation. In the absence of extensions beyond the Standard Model (SM) of particle physics (eg. with right-handed neutrinos), the Universe remains dominated by relativistic particles with an energy density decreasing as the fourth power of the temperature as the Universe expands. The number of relativistic degrees of freedom remains constant (g=106.75) until around 200  GeV, when the temperature of the Universe falls to the mass

Primordial black hole formation

There are a plethora of mechanisms for PBH formation. All of them require the generation of large overdensities, specified by the density contrast, δδρρ, usually assumed to be of inflationary origin. When overdensities re-enter the Hubble horizon, they collapse if they are larger than some threshold δc, which generally depends on the equation of state and density profile. However, there are other (non-inflationary) scenarios for PBH formation, where the inhomogeneities arise from first-order

Constraints

In this section, we discuss whether the PBH mass functions shown in Fig. 2, all of which assume fPBHtot=1, are compatible with the numerous observational constraints on fPBH(M). There is an underproduction of light PBHs for ñs0.955 and of heavy ones for

but we claim the mass distribution for ñs0.96 can provide 100% of the dark matter without violating any current reliable constraints, despite some claims to the contrary.

In order of increasing mass, the PBH constraints come from the

Observational conundra

Besides passing the current observational constraints on the form of the CDM, the PBH mass function with ñs0.96 predicted from the known thermal history of the Universe provides a unified explanation for several other puzzling conundra. We discuss these in order of increasing PBH mass. The status of some of the conundra is still unclear but we include all of them to convey the breadth of predictions.

Conclusions

Various cosmic conundra are naturally explained by the PBH mass function expected from the known thermal history of the Universe if fPBHtot=1, i.e. if PBHs constitute all of the dark matter. The current LIGO/Virgo run should measure the mass function of coalescing black holes rather precisely and, remarkably, two recent events coincide with the “proton” peak at around 1M, while a third corresponds to the “pion” plateau at around 50M. This is indicated in Fig. 2 and was a prediction of our

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors thank Y. Ali-Haïmoud, C. Byrnes, A. Green, M. Hawkins, K. Jedamzik, A. Kashlinsky, P. Mroz, J. Rich, C. Ringeval, D. Schwarz and Di Wen for stimulating discussions. B.C. thanks the Research Center for the Early Universe (RESCEU) at University of Tokyo for hospitality received during this work. J.G.-B. acknowledges support from the Research Project PGC2018-094773-B-C32 (MINECO-FEDER) and the Centro de Excelencia Severo Ochoa Program SEV-2016-0597. The work of S.C. is supported by

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