Leptogenesis and Planck-scale black hole remnants in a Pati-Salam cosmology

The universe is filled with two great mysteries that modern physics has yet to solve. The first is why there is more matter than antimatter. In the earliest moments after the Big Bang, matter and antimatter should have been created in equal amounts, only to annihilate each other and leave behind a sea of pure light. Yet, we exist. Something tipped the scales, creating a tiny surplus of matter that eventually formed stars, planets, and us. The second mystery is dark matter. Astronomers know that roughly a quarter of the universe is made of an invisible substance that holds galaxies together, but no one has ever seen a particle of it or knows what it is made of. For decades, scientists have tried to explain these two puzzles separately, often proposing complex new particles or forces. A recent study, however, suggests that the answer to both might lie in the same strange, tiny object: a primordial black hole.

These are not the massive black holes found at the centers of galaxies, which form from collapsing stars. Instead, they are microscopic black holes that could have formed in the first fraction of a second after the Big Bang, created by fluctuations in the density of the early universe. If they exist, they would be incredibly small, some weighing less than a gram, and they would be evaporating right now, releasing energy in a process known as Hawking radiation. A team of researchers has built a new model showing how these tiny black holes could have acted as cosmic factories, producing the heavy particles needed to create our matter-dominated universe while simultaneously leaving behind a stable residue that makes up the dark matter we see today.

The researchers worked within a specific theoretical framework called the Pati–Salam model. This is a way of organizing the fundamental particles of nature that treats the right-handed neutrino—a heavy, invisible cousin of the familiar neutrino—as a necessary part of the universe's structure rather than an optional add-on. In this model, the existence of these heavy neutrinos is tied to a specific energy scale where the forces of nature split apart. The team asked a simple but difficult question: could the evaporation of primordial black holes provide the heavy neutrinos needed to generate the matter-antimatter imbalance, and could the black holes themselves leave behind a remnant that serves as dark matter?

To answer this, they simulated the life cycle of these black holes. They started with a universe where the forces had already split apart before the rapid expansion of inflation began, ensuring that dangerous magnetic monopoles were diluted away. They then introduced a population of primordial black holes with a specific range of masses. As these black holes evaporated, they would spit out particles. If the black holes were hot enough, they would emit the heavy right-handed neutrinos. These neutrinos would then decay in a way that created a slight excess of matter over antimatter. This excess would eventually be converted into the baryons—the protons and neutrons—that make up all visible matter.

The study found that this process works, but only under very specific conditions. The researchers discovered a sharp divide based on the mass of the black holes. If the black holes were very light, weighing around one hundred grams or less, they would be hot enough to emit the heavy neutrinos directly. This would create a "non-thermal" source of matter, generating the baryon asymmetry without needing the universe to be extremely hot. However, this scenario hits a wall when considering dark matter. If these light black holes evaporate completely, they leave nothing behind. But if quantum gravity stops their evaporation just before they vanish, leaving behind a tiny, stable "remnant," the math breaks down. The study shows that if the black holes are light enough to create the matter asymmetry this way, the leftover remnants would be so numerous that they would overfill the universe with dark matter, far exceeding what we observe. In this specific scenario, the two goals—creating the right amount of matter and the right amount of dark matter—cannot be achieved at the same time.

The solution, the authors found, lies in slightly heavier black holes. If the primordial black holes weigh around one million grams, they are cooler and cannot emit the heavy neutrinos efficiently on their own. Instead, the heavy neutrinos are produced by the hot plasma of the early universe. The black holes then play a different role: they evaporate and dump a massive amount of entropy, or disorder, into the universe. This process dilutes the matter asymmetry that was already created, but it does not destroy it. Crucially, when these heavier black holes finally evaporate, they leave behind a stable remnant. Because the black holes are heavier, the number of remnants they leave behind is much smaller. The study calculates that for black holes with an initial mass of approximately one million grams, the number of remaining remnants perfectly matches the observed amount of dark matter in the universe.

This single mass value of about one million grams acts as a sweet spot. It is heavy enough that the remnants do not overpopulate the universe, yet it is light enough that the black holes evaporate early enough to allow the matter asymmetry to be processed by the universe's natural mechanisms before the forces of nature freeze out. The researchers also noted that this scenario leaves a distinct fingerprint. The random distribution of these black holes in the early universe would have created ripples in spacetime, generating a background hum of gravitational waves. These waves would have a frequency that future detectors, such as the Einstein Telescope, might be able to hear. Additionally, the direct emission of gravitons during the black holes' final moments would contribute to the radiation density of the universe, a quantity that future cosmic microwave background experiments could measure with high precision.

The paper concludes that while the idea of using black holes to solve both the matter and dark matter puzzles is compelling, it is not a universal fix. It rules out the possibility that the lightest black holes could do the job alone. Instead, it points to a specific, narrow window of black hole masses where the universe could have been tuned to produce exactly what we see today. The model relies on the assumption that quantum gravity halts the evaporation of black holes at the Planck scale, leaving behind stable remnants. If this assumption holds, then the existence of dark matter and the origin of our matter-filled universe are two sides of the same coin, forged in the evaporation of a specific population of primordial black holes. The findings suggest that the next generation of gravitational wave and cosmic background experiments could either confirm this elegant connection or force us to look for a different explanation for the dark side of the cosmos.