From Non-Thermal to Thermal: Cosmological Imprints of Self-Interacting Secluded Dark Matter

Dark matter is the invisible scaffolding of our universe. We know it is there because its gravity holds galaxies together and shapes the vast cosmic web, yet it refuses to interact with light or ordinary matter in any way we can easily detect. For decades, scientists have tried to understand what this substance is made of and how it behaved in the fiery moments after the Big Bang. A central question has been whether dark matter was ever "hot"—moving at speeds close to light—or "cold," moving slowly enough to clump together and form the seeds of galaxies. If it was too hot, it would have streamed away from dense regions, erasing the small structures we see today. This tension between the need for dark matter to be heavy enough to form galaxies and light enough to explain the universe's expansion has driven much of modern cosmology.

In a new study, researchers at the Indian Institute of Science Education and Research and the Saha Institute of Nuclear Physics have explored a specific scenario where dark matter behaves differently than previously thought. They focused on a type of dark matter that lives in a "secluded" sector, meaning it does not talk to the normal particles of the Standard Model, such as electrons or protons. Instead, this hidden sector has its own internal rules. The team imagined a universe where dark matter particles are created not from a hot soup of ordinary matter, but from the decay of a field called the inflaton, which drove the rapid expansion of the early universe. In this model, the dark matter particles start with a very specific, non-random speed distribution. The researchers then asked a simple but profound question: if these particles can bump into each other, will they eventually settle into a calm, thermal state, and what would that mean for the universe we see today?

To answer this, the scientists built a detailed computer simulation of the early universe. They tracked how a cloud of these invisible particles, born from the decay of the inflaton, evolved over time. Initially, the particles were not in equilibrium; they were moving in a way that did not resemble a standard gas. However, the researchers included a mechanism where these particles could scatter off one another, a process driven by a self-interaction force. By solving the complex equations that govern how particle distributions change in an expanding universe, they watched the system evolve. They found that if the particles interact with each other often enough, they do indeed thermalize. They redistribute their energy and settle into a stable state defined by a temperature and a chemical potential, which is a measure of how many particles are present relative to the energy available.

One of the most striking discoveries in this work is that this secluded dark matter can be significantly hotter than the ordinary matter in the universe, even while still satisfying all known cosmological constraints. In many previous theories, scientists assumed that if dark matter was secluded, it would be colder than the visible universe. This new study shows the opposite is possible. If the inflaton field was heavy enough compared to the temperature at which the universe reheated after inflation, the dark matter sector can end up with a higher temperature. The researchers found that this "hotter" state is allowed because the dark matter particles carry a negative chemical potential. In simple terms, this negative value acts as a brake on the energy density, preventing the dark matter from becoming so energetic that it would disrupt the formation of light elements in the early universe, a process known as Big Bang Nucleosynthesis.

The study also calculated the lower limits on the mass of these dark matter particles. Without the help of self-interactions, the particles would stream freely for a long time, washing out small-scale structures in the universe. This would require the particles to be relatively heavy to avoid erasing the tiny dwarf galaxies we observe. However, the researchers found that the act of thermalization itself changes the outcome. When the particles collide and exchange momentum, they effectively shorten the distance they can travel freely. This "free-streaming length" is reduced, which means the dark matter can be lighter than previously thought without destroying the cosmic structure. For a high reheating temperature scenario, the lower mass limit drops to roughly 2.2 times 10 to the power of negative 10 GeV. For a lower reheating temperature, the limit is about 0.47 GeV. These values are significantly lower than the limits found in scenarios where dark matter never interacts with itself, suggesting that the history of how dark matter was produced and how it cooled down is just as important as its final mass.

The work relies on numerical simulations to track the momentum of billions of particles as the universe expands. The researchers verified that their code correctly conserved the total number of particles and energy, ensuring that the thermalization process they observed was a genuine physical effect and not a mathematical artifact. They confirmed that the time it takes for the dark matter to reach this thermal state depends on the strength of the self-interaction. If the interaction is strong enough, the particles thermalize quickly, effectively "forgetting" their chaotic birth and settling into a smooth distribution. If the interaction is too weak, they remain in their initial, non-thermal state. The study maps out exactly where this transition happens, showing that for a wide range of plausible conditions, thermalization is a robust outcome.

Ultimately, this research reshapes how we view the constraints on dark matter. It demonstrates that the mass of dark matter is not fixed by a single universal rule but depends heavily on the specific history of the early universe, particularly the mass of the inflaton and the temperature at reheating. The findings suggest that the "warm" dark matter scenarios, which have long been constrained by observations of galaxy formation, might be viable in ways that were previously overlooked. By allowing for a hotter dark sector with a non-zero chemical potential, the universe can accommodate lighter dark matter particles that still form the galaxies we see today. This opens up a new window of possibilities for what dark matter could be, moving beyond the simple assumption that it must be cold and non-interacting, and highlighting the rich, complex physics that may have played out in the first moments of cosmic history.