I've been making my way through several papers and textbooks on the subject, but they all seem to gloss over this subject: how is the equilibrium of protons, neutrons and photons related to the expansion rate?
From what I've picked up on the subject, photons, protons and neutrons are all floating around in a hot soup. Protons are relatively stable, but neutrons decay in about 15 minutes. While the soup is dense, this isn't a problem as the photons readily interact with protons making and destroying neutrons in equal amounts.
But after the universe has expanded by a certain amount, the cross-section of the proton becomes diminished with respect to the size of the universe and the probability of a photon interacting with it drops. When the probability drops beyond a certain amount, new neutrons stop being created and we only have 15 minutes or so for the protons to join with the neutrons and become nuclei (either Deuterium, Helium or Lithium), or they decay into protons.
I'm sure I've got some of this wrong, so could someone please explain in plain English how the expansion rate of the Universe determines the ratio of Hydrogen to Helium. And what would happen if the expansion rate were slower or faster than FLRW.