The universe is like dough rising in an oven. Galaxies are flying apart, and the rate of this expansion is accelerating. To explain the accelerating expansion, cosmologists came up with dark energy — a mysterious force that pushes space apart from within. The standard recipe, called Lambda-CDM, works pretty well, but it has its inconsistencies.

The authors of the new study decided to rewrite the recipe, adding a fresh idea — fractional entropy. Ordinary entropy (a measure of disorder) grows with surface area, but here it is given a fractional exponent, as if measuring not in whole steps but in halves or quarters. From this fractional entropy, they derived three dark energy models, differing in the choice of horizon — an imaginary boundary beyond which light hasn't reached us yet. The first model uses the Hubble horizon (the distance at which galaxies recede at the speed of light), the second uses the future event horizon (what we will ever be able to see), and the third uses the particle horizon (what we have already seen in the past).

All three models were compared with observational data: supernova explosions, galaxy distribution, and the latest results from the DESI survey. It turned out that two models, with the Hubble horizon and the particle horizon, sharply disagree with data from the early universe, especially with temperature fluctuations in the cosmic microwave background. But the model with the future event horizon passed the test: today it is almost indistinguishable from the standard Lambda-CDM, but its deceleration parameter will behave differently in the future. This means that in billions of years, the expansion of the universe could follow a different scenario — slightly faster or slightly slower than the standard theory predicts.

It's too early to say which model is correct. But if future observations confirm deviations, it will be the first hint that dark energy is more complex than just a cosmological constant introduced by Einstein a hundred years ago.