The curvature and size of the Universe

[Jaime Rudas]

It could be said, but it would be wrong. The volume inside of a sphere in a positive curvature space is less than in a flat space.

But of course! I don't know what I was thinking!

 

[Jaime Rudas]

It could be said, but it would be wrong. The volume inside of a sphere in a positive curvature space is less than in a flat space.

If the universe is flat, the volume of the observable universe (radius Ro = 46 Gly) is:

$\dfrac 43 \pi R_0^3 = 407,720 ~ Gly^3$

What would be its volume if the universe is spherical with curvature radius Rc = 459Gly?

 

[Hornbein]

https://physics.stackexchange.com/questions/680076/how-do-we-calculate-a-volume-in-curved-space

There is this but it isn't intended for beginners and I don't understand it.

 

[Jaime Rudas]

If the universe is flat, the volume of the observable universe (radius Ro = 46 Gly) is:

$\dfrac 43 \pi R_0^3 = 407,720 ~ Gly^3$

What would be its volume if the universe is spherical with curvature radius Rc = 459Gly?

I found that the volume of a sphere in a 3-spherical space is:

$V(r)=2\pi R^3 \left ( \dfrac r R-\dfrac{\sin \dfrac{2 r}R}2 \right )$

Where r is the radius of the sphere and R is the radius of curvature of the 3-spherical space.

For r=46 Gly and R=459 Gly, V=406,902 Gly³

The derivation of the formula can be seen in:

https://forum.lawebdefisica.com/for...-en-geometría-no-euclidea?p=361848#post361848

 

[fresh_42]

Temporarily closed for moderation.

 

[DrClaude]

Thread has been cleaned up and is now reopened.

 

[PeterDonis]

And now the thread is closed again for moderation.