From what I have read one of the key pieces of evidence for the big bang theory is the ratio of hydrogen to helium in the universe. I have not seen any explanation as to how the big bang theory predicted this ratio (3:1 by mass).
How did the big bang theory make this prediction?
It seems like the prediction made by the big bang theory would explain why there is more hydrogen than helium, but not how much more.
If the answer is based on our knowledge of the temperature and size of the universe in the first few fractions of seconds after the big bang, how do we know the time frame of those events in the first place?
Best Answer
Cosmologists think they understand how the scale factor of the universe has grown with time, based on the Friedmann equations. They also think they understand how the temperature of the universe has cooled as the universe expanded. Finally, they can measure the current temperature of the universe by measuring the frequency distribution of the cosmic microwave background radiation.
So, knowing the current temperature and using equations to extrapolate backwards in time, they come up with temperatures like one billion K at 10 seconds after the Big Bang. This corresponds to a modest energy per particle of 100 keV. I say “modest” because nuclear physicists understand very well how nuclei behave at such energies; nuclear physicists have collided nuclei at such energies for decades.
So the reactions involved in nucleosynthesis have been studied in the laboratory, and the cross section for, say, a proton and a neutron to form deuterium, and the cross section for deuterium and a proton to form Helium-3 are known.
The last piece of the puzzle is knowing the baryon density at that time after the Big Bang. This is extrapolated backward from the current observed baryon density.
If you know the density of protons and neutrons and the cross sections for nuclear reactions, you can do a computer simulation that predicts the abundances of the elements formed during Big Bang nucleosynthesis.
Any uncertainty about the Big Bang is about what happened in the very early universe, say in the first trillionth of a trillionth of a second. But this is way before the time of nucleosynthesis. By the time the universe was baking helium, its physics is believed to be well-understood.