# How large was the universe at the start of BBN? How large was it after?

I'm trying to get a handle on the basics of BBN. I've read several authors quote the figure of 17 minutes. So BBN started at 3 minutes and ended at 20 minutes after the start of time. So how large was the when the process started and how large was it when it ended? How did they arrive at this value of 17 minutes?

• The Big Bang didn't happen at a point so it is meaningless to ask how big the universe was 7 minutes after the Big Bang. However you can ask about the temperature and density as a function of time, and the 17 minutes refers to the time at which the temperature had cooled enough for nuclei to form. – John Rennie Nov 6 '18 at 17:24
• The size of the universe is meaningless only for an open universe in the Friedmann model, but is meaningful for a closed universe in this and other models and even for an open universe in other models (like the Milne model). – safesphere Nov 6 '18 at 18:00
• Are you asking what was the size of our currently observable universe during that epoch? – PM 2Ring Nov 6 '18 at 18:05
• @JohnRennie - Several explanations I've read state that the rate of expansion was critical to the %75 / %25 split between H and He. How can you talk about a rate of expansion if you can't talk about the size difference between 3 and 20 minutes? – Donald Airey Nov 7 '18 at 1:23
• @DonaldAirey the expansion is characterised by a scale factor that tells us by what factor the universe has expanded. This is directly related to the average density and temperature, which are what control nucleosynthesis. But this is not a size. For example if the universe is infinite it has always been infinite right back to the Big Bang. The term size is sometimes used as a shorthand for the size of the currently observable region of the universe, and this is just the current size multiplied by the scale factor. – John Rennie Nov 7 '18 at 5:14

According to Wikipedia’s “Chronology of the universe”, the radius of what has become our observable universe, at the end of the Big Bang nucleosynthesis era, was about 300 light years. At that time the universe was radiation-dominated and therefore the radius was expanding as $$t^{1/2}$$ so the radius would have been smaller by a factor of $$\sqrt{3/20}=0.39$$ at 3 minutes compared with 20 minutes.