What calculations are needed to determine the temperature of the universe at the beginning of time/moment of the big bang? Had this on a physic’s test ~1975 and can’t remember how to do it anymore. Can anyone help? tks,dr
You can’t really talk about the temperature at the “moment of the Big Bang”, since if you try to extrapolate the temperature backwards, you conclude that it was infinite at that moment. We physicists don’t like infinities in our calculations, so we strongly suspect that we don’t completely understand what was going on back then.
As the Universe expanded, the temperature cooled; roughly speaking, I believe that the temperature is inversely proportional to the scale factor of the Universe (basically, the “size” of the Universe). The scale factor was proportional to the square root of the time since the Big Bang in the early universe (the “radiation-dominated” era), but later transitioned to a regime where it was proportional to the 2/3 power of the time since the Big Bang (the “matter-dominated” era), and then transitioned to a regime where it grew exponentially with time (the current “dark-energy-dominated” era.) If you wanted to, you could use these facts to extrapolate the temperature back from the current 2.7 K temperature of the Universe to any earlier time, though it’d only be an order-of-magnitude estimate. And, as noted above, you can’t extrapolate back to t = 0.