The cosmic abundance of helium reinforces ideas about the temporal evolution of the temperature of the universe. The estimated primordial He/H ratio (found by looking at very low metallicity galaxies) matches the predictions of the hot big bang model and fails to be explained by alternatives such as the steady state theory.
If the universe was once hot enough ($>10^{11}$ K) that neutrons and protons existed in a thermal equilibrium, but subsequently expanded and cooled, then the He/H ratio is largely set by four things. (i) the mass difference between the neutron and proton; (ii) the decay timescale of a free neutron; (iii) the temperature range in which stable deuterium can exist without breaking apart or fusing into helium, (iv) the reaction rates for the equilibrium reactions betweenprotons, neutrons and protons in the early universedeuterium nuclei, which depends weakly on the ratio of baryons to photons.
The sequence of events is detailed in What is the reason for the shift in balance between neutrons and protons in the early universe? . In summary: the mass difference between the neutron and proton determines that at the epoch that they fall out of thermal equilibrium, their ratio is about 1:6. All the neutrons would subsequently decay, but for the next 200 s or so, the universe is cool enough for deuterium to form and hot enough for deuterium fusion to form helium. During this time a few more free neutrons decay, driving the final n:p ratio to 1:7 by the time the universe cools below the temperature required for further nuclear reactions.
The big bang model perfectly explains these results with only one free parameter - the ratio of baryons to photons, which determines (weakly) the exact time/temperature at which the neutrons and protons fall outfraction of thermal equilibriumfree neutrons that end up forming deuterium nuclei (and then helium) as opposed to freely decaying. However, the primordial deuterium abundance also depends on this parameter in a different (and more sensitive) way. That the estimated primordial He/H and D/H can be reproduced at with the same baryon to photon ratio is what strongly supports the big bang model.