# How is the scale factor from the FLRW equation used with Volume?

I'm trying to put a spreadsheet together that shows the co-moving volume of the universe from the time soon after the Big Bang through the present and then as predicted into the future. I am pretty sure that all I have to do is use the scale factor $a(t)$ as derived from the FLRW equations (I suppose this is what the scale factor is for anyway). How is the scale factor meant to be used with the volume if I want to calculate $V(t)$?

1 - Is it , $V(t) = V_0 a(t)^3$?

2 - Is it simply, $V(t) = V_0 a(t)$?

3 - Or $R(t) = a(t) R_0$ and then find $V(t)$ from $R(t)$?

• It just depends whether you are interested in the comoving volume or the physical one, which are related as outlined in the answer. – Danu Jun 20 '14 at 14:27
• Note that the co-moving volume is unchanging by definition, since it is defined $V(t)/a(t)^3$. What you're trying to compute is the physical volume. – Kyle Oman Jun 20 '14 at 14:34

## 1 Answer

The first option is the right. Comoving distances are related to physical ones as $l_{phys}=al_{com}$. Then, for a volume, which always have a product of three distances, you will always get $V_{phys}=a^3 V_{com}$.