The Universe after the Big Bang was almost perfectly homogeneous. Almost, because tiny density perturbations stretched by inflation became the seeds of galaxies. But what if these same perturbations could give birth not only to stars but also to black holes? Not ordinary ones, but primordial: objects that emerged in the first moments when the Universe was hot and dense. They remain a mystery to this day.

The idea is simple: if in some region the density was slightly above the critical value, that region could collapse directly into a black hole. But standard inflationary models produce perturbations that are too weak on small scales. An amplifier is needed. And as the authors of the new work show, the magnetic field could have been such an amplifier.

The magnetic field acts as an invisible sculptor, shaping black holes out of the early Universe. In the early Universe, before the first atoms appeared, the electromagnetic field could behave unusually. If its coupling to gravity was briefly broken, magnetic fields were born. These, in turn, created additional inhomogeneities. And here is the key point: magnetic fields did not just add energy; they pressed unevenly, creating anisotropic stresses (unequal pressure in different directions). This amplified curvature perturbations (density inhomogeneities stretched by inflation) to a level where collapse into a black hole becomes inevitable.

The authors considered a specific magnetogenesis model (the birth of magnetic fields in the early Universe) with a so-called sawtooth coupling function. It grows during inflation, reaches a peak, and then decreases, restoring standard electrodynamics. This profile yields a magnetic field spectrum with a break: on large scales it matches the observed intergalactic fields, while on small scales it sharply intensifies, giving rise to black holes.

The results are impressive. For a reheating temperature $T_{re}$ ≈ 2×10⁵ GeV and a spectral index (the slope index of the power spectrum) $n_B$ = 2.674, the model gives a fraction of primordial black holes in dark matter $f_{PBH}$ ≈ 1, meaning virtually all dark matter. The mass of such black holes is about 4×10⁻¹⁶ solar masses. That is roughly the mass of an asteroid. Such objects are invisible, but their gravitational influence can be sought.

The abundance of black holes is exponentially sensitive to the spectral index of the magnetic field: a change in $n_B$ of just 0.005 changes $f_{PBH}$ by several orders of magnitude. This makes the model testable: precise measurements of magnetic fields on different scales would suffice.

A bonus: gravitational waves. The anisotropic stresses of the magnetic field generate a stochastic gravitational wave background. Its peak amplitude for the benchmark point BP1 ($T_{re}$ = 1 GeV, $n_B$ = 2.28) is $Ω_{GW}$ h² ≈ 2.05×10⁻⁹. This is right within the sensitivity range of future detectors LISA, DECIGO, BBO, and SKA. If this background is detected, it would be an independent confirmation of magnetogenesis.

The work unites two seemingly unrelated problems: the origin of cosmic magnetic fields and the nature of dark matter. The same process, the birth of magnetic fields in the early Universe, explains both. Previously, it was unclear whether primordial magnetic fields could simultaneously match observations and amplify perturbations to the required level. Now it is shown that they can, and without fine-tuning of the inflationary potential. A sawtooth coupling function suffices.

What next? First, a more accurate account of magnetohydrodynamic effects on small scales. Second, investigation of other forms of the coupling function. Third, joint analysis of data from future gravitational wave observatories and constraints on the abundance of primordial black holes. This will narrow down the model parameters and perhaps finally solve the dark matter puzzle.

The Universe we see is just the tip of the iceberg. Beneath it lies invisible matter, and possibly invisible black holes. The magnetic field that once filled the cosmos could have sculpted them from the primordial chaos. Now we have a way to test this.