# How much does the volume of our universe increase by as it expands?

Jul 29, 2016

See explanation for points to ponder.

#### Explanation:

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

t.

' 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

$\left(\left(\frac{4}{3}\right) \pi {a}^{3}\right) '$

$= 4 \pi {a}^{2} = 12.57$square light year/year.

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.

Reference:

A.S.Adikesavan, The rate of change of Hypervolume is Hypersurface, Math. Student, 1972, pp 305-307.