In the time period between about 100 seconds and 30 minutes after the Big Bang, but mostly with the first three minutes, the temperature and density of the universe were appropriate for the efficient synthesis of the light elements. Just as in the Sun, some of the hydrogen nuclei were underwent fusion to form heavier nuclei including helium nuclei. This was the era of primordial nucleosynthesis. The current abundances of the light elements reflect what occurred during the epoch of primordial nucleosynthesis and therefore place strong constraints on the state of the universe and the baryon density during that time.
We know that the universe today contains about 23% of its mass in helium (about almost 10% by number; remember that 1 helium nucleus has about 4 times the mass of a hydrogen nucleus). In fact, all the helium production in stars isn't very important compared to the production in the first three minutes after the Big Bang. During that era, conditions had to be just right so that we wound up with a universe that has 9 hydrogen nuclei for every 1 helium nucleus. If conditions had been different, we wouldn't have wound up with that ratio.
Also, we know that most of the hydrogen in the universe is in the form of simple hydrogen, not its heavier isotopes deuterium or tritium. Deuterium is not produced in stars; it is only destroyed. Therefore the abundance of deuterium today places a lower limit on the amount of deuterium produced in the epoch of primordial nucleosynthesis, and thus on the density of baryons.
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