$SU(\mathcal{N})$ baryon formation in the early Universe and dark matter

In the vast, invisible architecture of the universe, there is a persistent mystery regarding the nature of dark matter. While we can see stars and galaxies, the majority of the universe's mass remains hidden, exerting gravity but refusing to emit or reflect light. For decades, physicists have proposed that this missing mass consists of undiscovered particles, often imagining them as simple, solitary entities. However, another compelling idea suggests that dark matter might be made of complex, composite structures, much like the protons and neutrons that form the atoms of our own bodies. These hypothetical particles would be "baryons" formed from a new type of force that binds them together, similar to how the strong nuclear force holds quarks together in our world. The critical question for cosmologists is how these complex structures could have formed in the chaotic, high-energy environment of the early universe without being destroyed before they could ever become the dark matter we observe today.

A team of researchers has now investigated this formation process for a specific class of theories where the binding force involves a large number of "colors," a property analogous to the electric charge but specific to this new force. In our familiar world, the force that binds quarks comes in three varieties, allowing them to combine into groups of three to form stable particles. The researchers explored what would happen if this force came in many more varieties—specifically, twelve, eighteen, or even twenty-one. They set out to simulate the moment when the universe cooled down enough for these forces to snap into action, trapping free-floating particles into bound states. Their goal was to determine whether these complex particles could successfully assemble into stable, neutral dark matter candidates, or if the process would be blocked by the very nature of the forces involved.

The simulation revealed a significant obstacle that arises when the number of force varieties increases. In the early universe, as the temperature dropped, free particles began to clump together. The researchers found that while particles could easily pair up to form simple, two-particle structures known as mesons, the path to building the larger, multi-particle baryons was severely hindered. This blockage occurs because the force that pulls a single particle into a growing cluster is much weaker than the force that pulls a particle and an anti-particle together to form a meson. As a result, the building blocks for the large baryons are rapidly consumed by the formation of mesons. The researchers describe this as a "bottleneck": the assembly line for the complex dark matter particles is clogged because the ingredients are being diverted into simpler, competing structures before the larger construction can be completed.

This effect becomes dramatically stronger as the number of force varieties increases. In the case of twelve varieties, the researchers calculated that the number of successful baryons formed is suppressed to a tiny fraction of what would be expected in a simpler system. For eighteen varieties, the suppression is even more extreme, reducing the yield by a factor of ten to the power of twenty-three. This means that for these larger systems, the universe produces almost no stable baryons at all. The few that do form are so rare that, to account for the total amount of dark matter we observe today, each individual particle would need to be incredibly massive. In fact, for the largest numbers of varieties studied, the required mass would exceed the theoretical limits set by the laws of quantum mechanics, suggesting that such heavy particles simply cannot exist in the way the model describes.

To make their model realistic, the researchers also ensured that the particles could interact with the known forces of nature in a way that allows unstable particles to decay safely. They constructed a scenario with three types of particles, similar to the up, down, and strange quarks in our own world, which allows for the existence of a neutral, stable baryon that could serve as dark matter. In this setup, any unstable or charged versions of these particles would decay into harmless radiation long before the formation of the first stars, ensuring they do not interfere with the known history of the universe. The study confirms that while a neutral, stable dark matter particle is theoretically possible in these models, the mechanism that creates it is so inefficient for large numbers of force varieties that the resulting particles would be far too heavy to be viable candidates for the dark matter that fills our cosmos.

The implications of this work are profound for theories that rely on complex, composite dark matter. It suggests that if dark matter is indeed made of such structures, the underlying force cannot have too many varieties, or the universe would simply fail to produce enough of them. For models with a moderate number of varieties, such as twelve, a stable dark matter candidate could exist, but it would need to be extremely heavy, weighing in at roughly one hundred thousand times the mass of a proton. This places strict constraints on how these theories can be built and tested. The researchers conclude that while the idea of composite dark matter remains a fascinating possibility, the specific mechanism of its formation acts as a powerful filter, ruling out the most complex versions of the theory and pointing toward a much narrower path for future exploration.