The universe is expanding, and the rate of that expansion is a hot topic in cosmology. Nearly a century ago, Edwin Hubble discovered that galaxies are flying apart, but modern measurements of the Hubble constant, which characterizes the expansion rate, give conflicting values. This discrepancy might be resolved by interactions between dark matter and dark energy, the mysterious substances that together make up about 95% of everything in the cosmos. A new theoretical model describes them not as immutable entities but as components that can transform into each other, much like a reversible chemical reaction where reactants and products exist in dynamic equilibrium.

The researchers applied the Boltzmann equation, a mathematical tool traditionally used to describe the collision rates of atoms in a gas, to the so-called dark sector. In this context, it allowed them to calculate how the "particles" of dark matter and dark energy are distributed and evolve, and it showed that mutual transitions between them are not a fitting parameter but a natural consequence of particle physics, given certain types of interactions. Testing the model against observational data from telescopes confirmed its agreement with the real picture and yielded a specific value for the expansion rate: 67.7 km/s per megaparsec (the Hubble constant).

Interestingly, the frequency of these transformations turns out to be minuscule: calculations indicate that over the entire lifetime of the visible universe—13.8 billion years — no more than a couple of thousand such events could have occurred. This extreme rarity naturally explains why we don't detect them directly, and it also imposes strict constraints on future theories, forcing them to predict an equally slow reaction between dark matter and dark energy.