Two black holes merging into one.
Artist’s impression of merging black holes in clusters. Credit: Ingrid Bourgault.


There are numerous cosmic conundra — most prominently the nature of dark matter and dark energy. But there are several others concerning (1) unexplained microlensing events by planet-mass objects with about 1% of the dark matter density; (2) microlensing of quasars, having a misalignment with the lensing galaxy such that the probability of lensing by a star is very low; (3) the high number of microlensing events by objects between two and five solar masses; (4) correlations in the X-ray and cosmic infrared background fluctuations; (5) non-observations of certain ultrafaint dwarf galaxies; (6) masses, spins and coalescence rates for black holes found by LIGO/Virgo; (7) the relationship between the mass of a galaxy and that of its central black hole.

In this brief article I report on a paper written jointly with Bernard Carr, Sébastien Clesse and Juan García-Bellido. Therein we present a scenario which simultaneously addresses all of the above conundra (1 – 7) alongside with providing a natural explanation to the dark matter. In view of the gravitational-wave events from binary black-hole mergers, recently announced by the LIGO/Virgo collaborations, I focus on the resolution of conundrum (6), after a brief discussion of the model and the environment within which it makes its predictions.


Black holes and how they are generated are central to the studied scenario. Specifically, we discuss a broad class of models, being responsible for the expansion of the Universe, which also lead to an increase of small-scale fluctuations. This utilises the very same and well-understood mechanism which leads to the formation of large-scale structure, ie. patterns of galaxies and matter being much larger than individual galaxies, out of these initially small fluctuations.

Our model produces small-scale fluctuations which are so large that they collapse to black holes. As this happens very early in the Universe, ie. during its first three minutes, these black holes are called primordial black holes. The environment in which they form contains mostly radiation; the associated radiation pressure works against the gravitational collapse.

Thermal history of the Universe

We noticed that there are several instances during the evolution of the Universe when the pressure was reduced. This happens for instance during phase transitions of which there is one prominent one -- the so-called quantum chromodynamic phase transition. In general, when particles become non-relativistic — as happens every time the temperature of the Universe drops below their mass — the equation of state of the background plasma, and in turn the pressure, changes. As one of us (Bernard Carr) had shown many years ago, this enhances primordial black-hole formation exponentially.

A rough measure for the mass of these black holes is the mass contained in the region their initial fluctuation occupies just before it collapses. The striking observation we made was that those masses linked to the thermal history of the Universe are in location as well as in relative magnitude such that all of the conundra (1 – 7) can be simultaneously resolved. Furthermore, our model provides the entirety of the dark matter in the form of primordial black holes! Below, I shall focus on the explanation of the recent gravitational-wave events from LIGO’s recent (O3) run.

Gravitational Waves

Those events may constitute a turning point in gravitational-wave astronomy as these are of unexpectedly low (GW190425), large (GW190521), or different (GW190814) initial masses. Now, the beauty of our model is that it naturally predicted peaks in the mass distribution of expected black-hole detections at precisely these masses! Figure 2 shows the LIGO detection probability as a function of the two masses of the merging black holes. As can be seen, all of the three events lie near the forecasted maxima, suggesting that the nature of the dark matter might just have been unveiled. 

Plot showing the probability of detecting merging black holes as a function of their masses.
LIGO detection probability for two merging black holes of mass m1 and m2. Also shown are the gravitational-wave events GW190425, GW190814 and GW190521.


Further Reading

Primordial Black Holes as Dark Matter: Recent Developments

GW190425: Observation of a Compact Binary Coalescence with Total Mass ~ 3.4 M☉

GW190814: Gravitational Waves from the Coalescence of a 23 Solar Mass Black Hole with a 2.6 Solar Mass Compact Object

Properties and astrophysical implications of the 150 M☉ binary black hole merger GW190521