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A pot of boiling soup that suddenly starts cooling at a breakneck pace: that's roughly what the universe looked like a few minutes after the Big Bang. As the temperature dropped, the first nuclei began to stick together from protons and neutrons: hydrogen, helium, deuterium, and lithium. This process is called primordial nucleosynthesis, and its results are like a cookbook. Knowing how much of each ingredient was produced lets us check whether we truly understand the recipe for expansion.

But what if there's a typo in the book? The authors tested three cosmological models where the entropy (a measure of disorder) of the universe's horizon behaves non-standardly. The horizon is an imaginary boundary beyond which we can't see, because light from there hasn't reached us yet. In the new models, its entropy grows faster or slower than usual, which means the expansion rate should also change. To check whether this would break the early universe, the scientists calculated how the neutron freeze-out temperature, the moment when reactions involving neutrons slow down dramatically, shifts, and how much helium and deuterium form afterward.

Constraints from helium and deuterium turned out to be rather loose — almost all variants pass. But the neutron freeze-out temperature cuts off the boldest assumptions, leaving only a narrow corridor of allowed values. Lithium, as always, stands out: its observed abundance in old stars is lower than predicted, and this puzzle — the "cosmological lithium problem"—remains unsolved. However, the new models don't make it worse.

Now for the main surprise. The parameters these models need to explain today's accelerated expansion (what we call dark energy) fall right within the allowed zone. In other words, the same setting works both for the scorching soup of the first minutes and for the cold recession of galaxies today. It's as if one key fit both the front door lock and a safe — a rare and valuable coincidence that speaks to the models' internal consistency.

So the kitchen scale of primordial nucleosynthesis has confirmed: the recipe with modified horizon entropy doesn't spoil the dish. That means we can more boldly explore how these ideas might play out in other cosmic epochs.