A relook at a low reheating temperature: Freeze-in versus Freeze-out

Dark matter is the invisible scaffolding that holds the universe together, making up roughly eighty-five percent of all matter, yet its true nature remains one of the greatest mysteries in science. We know it exists because of how its gravity pulls on stars and galaxies, but we have never directly seen a particle of it, nor do we know how it came to be. For decades, physicists have assumed that in the early moments after the Big Bang, the universe was a seething, super-hot soup of particles. In this standard view, dark matter particles either formed and then stopped interacting as the universe cooled, or they slowly leaked into existence from the hot soup. Both scenarios rely on the universe being incredibly hot right from the start, a condition known as a high reheating temperature, which sets the stage for all subsequent cosmic history.

A new study by researchers at the University of Delhi and the Indian Institute of Technology Kanpur challenges the idea that this initial heat must be extreme to explain the amount of dark matter we see today. They asked a simple but profound question: what if the universe never got that hot? Specifically, they investigated a scenario where the thermal bath of particles that fills the universe only begins to exist at a relatively low temperature, far cooler than the trillions of degrees usually assumed. By running detailed simulations of how dark matter would behave under these cooler conditions, they discovered that a low starting temperature does not just tweak the numbers; it can fundamentally break the mechanisms that create dark matter. Their work suggests that if the universe started too cool, there would be no way to produce the correct amount of dark matter, regardless of how the particles interact, effectively setting a hard lower limit on how cold the early universe could have been.

To understand the significance of this finding, one must first grasp the two main ways scientists think dark matter was created. The first method, called freeze-out, imagines dark matter particles as neighbors in a crowded room who are constantly bumping into each other. When the room is hot and crowded, they interact frequently. As the room cools and the crowd thins, they stop bumping into each other and freeze in place, leaving a specific number of survivors. The second method, freeze-in, is more like a slow leak. Here, dark matter particles are so shy that they barely interact with the hot soup of normal matter. They are produced very slowly over time, trickling into existence until the universe cools enough that the production stops. Both methods depend heavily on the temperature of the universe, but they react to a drop in temperature in very different ways.

The researchers built a simplified model to test these ideas, using a stable particle of dark matter and a heavy carrier particle that acts as a bridge between the dark world and the visible world. They assumed that the universe was created instantly at a specific temperature, rather than gradually heating up, and then watched how the dark matter abundance changed as they lowered that starting temperature. They found that for the freeze-in method, the temperature acts as a ceiling on production. If the universe starts at a high temperature, the hot soup has enough energy to create dark matter through various channels, including the decay of the heavy carrier particle. However, as the starting temperature is lowered, the energy available to create these particles shrinks. The researchers showed that this does not just reduce the amount of dark matter slightly; it can cut off the most efficient production channels entirely. For instance, if the starting temperature drops below the mass of the carrier particle, that particle can no longer be created on its own, forcing the universe to rely on much less efficient methods that struggle to produce enough dark matter to match what we observe today.

The situation is even more restrictive for the freeze-out method. In this scenario, the dark matter particles need to be hot enough and dense enough to interact with each other frequently before they freeze out. If the universe starts at a temperature that is too low, the particles never get a chance to reach a state of balance where they can interact properly. They simply never form the necessary equilibrium, and the process that usually leaves the correct amount of dark matter never gets off the ground. The study demonstrates that for a given set of particle properties, there is a minimum temperature below which the universe cannot produce the observed amount of dark matter, no matter how the scientists adjust the strength of the interactions between the particles. It is not a matter of tuning a dial to get the right number; below a certain threshold, the solution simply ceases to exist.

This finding overturns a popular misconception that lowering the reheating temperature is a flexible tool that can be used to fix problems in dark matter models. While it is true that a lower temperature can suppress the production of dark matter, the researchers showed that this suppression has a hard floor. They found that for any specific type of dark matter model, there is a critical temperature, determined by the masses of the particles involved, below which the relic abundance falls to minuscule levels. If the universe had started any cooler than this limit, the dark matter we see today would not exist in the quantities we measure. This means that the requirement to have the right amount of dark matter actually places a strict lower bound on the temperature of the early universe.

The study also explored the transition between these two creation methods. At high temperatures, a model can often support both a weakly interacting freeze-in scenario and a strongly interacting freeze-out scenario, depending on how the particles are tuned. However, as the starting temperature is lowered, the weakly interacting path becomes less efficient, requiring stronger interactions to compensate. Eventually, the temperature drops so low that even the strongest possible interactions cannot produce enough dark matter through freeze-in, while the conditions for freeze-out are never met because the universe is too cool to establish equilibrium. The two paths, which are distinct at high temperatures, converge and then disappear entirely below a critical temperature. This convergence reveals a fundamental constraint: the history of the universe's temperature is not just a backdrop for particle physics; it is a gatekeeper that determines which particle models are even possible.

By mapping out these limits, the researchers have provided a new way to look at the early universe. Instead of treating the reheating temperature as an arbitrary number that can be adjusted to fit a theory, they show that the existence of dark matter itself acts as a thermometer for the early cosmos. If we can identify the specific properties of dark matter particles in the future, such as their mass and how they interact, we could use the findings from this study to calculate the minimum temperature at which the universe must have been established. This turns the search for dark matter into a probe of the universe's thermal history, allowing physicists to infer conditions from billions of years ago based on the particles we hope to find today. The work suggests that the universe had to be hot enough to allow dark matter to form, and if it was any cooler, the cosmos would look very different from the one we inhabit.