What was the size of the universe around 400 million years after the Big Bang? I was trying to find out how large the universe was around 400 million years after the Big Bang as this is when some of the first galaxies were formed but I am having trouble finding out the answer or working it out.
I found some information on the size of the universe after 380,000 years when the CMB was created and by calculating the red shift from the time of creation a size of roughly 80 million light years is given by reducing the observable universes size by a factor of 1100 but I am not sure how to use this to calculate the universes size after 400 million years and I am not sure if as the above calculation is for the observable universe how that related to the actual size.
Is the size of the universe in terms of its length or diameter known or can be calculated after 400 million years from the Big Bang event?
There are two issues: what counts as &quot;the size of the universe&quot;, and how to rescale this. The second issue is easier.
If you have something at distance $d_1$ at time $t_1$ it will be at distance $d_2 = d_1 a(t_2)/a(t_1)$ at time $t_2$, where $a(t)$ is the scale factor at the relevant time. To further make things nice, $a(t)=1/(1+z)$ where $z$ is the redshift at the time.
For $\approx 400$ myr and a flat universe, $z=11.35$ and $a=0.081$ (from this calculator).
Note the word &quot;flat&quot; above: flat and open universes are by default unbounded. So in a literal sense they are always infinitely large. However, it is entirely possible that they have a nontrivial topology (imagine a universe that repeats like a hall of mirrors; various cases are possible), except that there is at present no evidence for this possibility - if there is something like going on it is likely larger than our current cosmological horizon.
The observable universe on the other hand is finite, and grows both because light from more and more distant objects arrive and because of the expansion makes their distance larger. This is why the size is not just $ct$, it depends on the expansion. The calculator gives 367.92 Mpc as the distance to the horizon at $z=11.35$, or 1.2 giga-lightyear.