$\mu$DM: a new mechanism for the baryon-dark matter coincidence

The universe is built on two very different kinds of matter. One is the stuff we can see and touch, the atoms that make up stars, planets, and people. The other is dark matter, an invisible substance that does not emit light but exerts a gravitational pull strong enough to hold galaxies together. For decades, astronomers have measured how much of each exists. The result is a puzzling coincidence: there is roughly five times more dark matter than ordinary matter. This ratio is so precise that it feels like a clue rather than a random accident. If the two types of matter were created by completely separate, unrelated processes, such a specific balance would be incredibly unlikely. Physicists have long searched for a mechanism that links the creation of these two substances, suggesting that their abundances are not independent but are instead tied together by a deeper law of nature.

A new proposal from a researcher at Tokyo Metropolitan University offers a fresh way to understand this connection. The paper introduces a concept called "chemical-potential-matched dark matter," or µDM for short. In this model, the invisible dark matter and the visible matter are not just neighbors in the cosmos; they are linked by a shared physical condition that existed in the early universe. The researcher suggests that the amount of dark matter we see today is directly determined by the same physical factor that set the amount of ordinary matter. This factor is a kind of pressure or bias, known in physics as a chemical potential, which acted on the universe just after the Big Bang. When the conditions of the early universe were right, this bias naturally forced the ratio of dark matter to ordinary matter to settle at the value we observe today, roughly 5.36 to 1.

The mechanism relies on a specific type of dark matter that behaves differently from the standard theories. Usually, if a particle is light and was created in a hot, dense environment, it would move so fast that it would wash out the clumps of matter needed to form galaxies. This is the problem with "hot" dark matter. However, this new model proposes that the dark matter particles were produced in a way that allowed them to be heavy enough to form structures but light enough to fit the mass range suggested by the coincidence. The paper suggests these particles could be very light, with masses between the energy of an electron volt and a thousand electron volts. This is incredibly light compared to a proton, yet heavy enough to be a viable candidate for the dark matter that shapes our universe.

To make this work, the researcher describes a scenario involving a field, which is like an invisible fluid filling space, that was rotating in the early universe. As this field rotated, it created a bias that pushed the creation of ordinary matter in one direction. At the same time, the ripples or excitations in this same rotating field became the dark matter particles. Because both the bias that created the ordinary matter and the particles that became dark matter came from the same rotating source, their final amounts are mathematically locked together. The rotation speed of this field determines the mass of the dark matter, and the strength of the bias determines the amount of ordinary matter. When the math is worked out, the ratio between them naturally comes out to be the five-to-one ratio that astronomers measure.

The paper explores two main ways this could happen. One involves a hypothetical particle similar to an axion, which is a very light particle proposed to solve other problems in physics. If these particles formed walls in the early universe, the movement of these walls could have created the necessary bias. The second, and primary, example involves a field that behaves like a complex wave. As this wave rotates, it generates the bias needed to create the matter imbalance. The paper shows that for this to work, the dark matter must have a mass in the range of a few electron volts to a few thousand electron volts. If the universe underwent a period of rapid expansion that diluted the density of everything after these particles were created, the dark matter could be slightly heavier, up to the mass of a million electron volts.

This idea is not just a theoretical guess; it is a specific model that can be tested. The researcher points out that if this theory is correct, the dark matter particles should be light enough to be detected by future experiments. Instruments like the NIRSpec spectrograph on the James Webb Space Telescope, or specialized searches for weakly interacting particles, could potentially find these particles or the signals they leave behind. The model also suggests that the process that created the dark matter might have left traces in the way the universe expanded or in the properties of neutrinos, the ghostly particles that pass through everything. By looking for these specific signatures, scientists could confirm whether the dark matter and ordinary matter are indeed twins born from the same rotating field.

The proposal also addresses why this dark matter does not destroy the structure of the universe. Even though the particles are light, the paper explains that they could have been produced in a way that makes them move slowly, behaving like "cold" dark matter rather than "hot" dark matter. This happens if the production process is boosted by a quantum effect that concentrates the particles into a slow-moving state. Alternatively, if the universe expanded rapidly after the particles were made, it would have slowed them down, allowing them to clump together and form the galaxies we see today. This flexibility means the model can fit with what we know about the formation of cosmic structures.

Ultimately, this work offers a new path to solving one of cosmology's oldest mysteries. It suggests that the strange balance between the visible and invisible parts of the universe is not a coincidence but a necessary outcome of a single physical process. By linking the mass of dark matter to the chemical conditions that created the matter in our bodies, the model provides a unified picture of how the universe came to be. While the idea is still a proposal and requires further testing, it demonstrates that the answer to the dark matter mystery might lie in a simple, elegant connection between the two halves of our cosmic inventory. The next step is to see if the universe agrees with this calculation by looking for the light, slow-moving particles that this theory predicts.