How much does the volume of our universe increase by as it expands?
See explanation for points to ponder.
For radius, the average rate is 1 light year / year
For this purpose, I assume that our universe is a 4-D (x, y, z, t)-
hypersphere x^2+y^2+z^2+t^2=a^2, where x, y, z, a are functions of
' denotes differentiation with respect to t.
Now, a = 13.77 light years and a'=1 light tear/year, nearly.
The rate of change of volume is surface area of hypersphere.
For 3-D sphere, volume expansion rate is
I have given points to ponder. I do not claim that this is definitive.
Yet, this paves the way for further research on these rates.
A.S.Adikesavan, The rate of change of Hypervolume is Hypersurface, Math. Student, 1972, pp 305-307.