2D Model of the Universe as an expanding ball

[darkdave3000]

TL;DR Summary

Can an expanding ball describe our universe in a simplified 2D model?

Can a simplified 2D model of our universe be an expanding ball? Where the surface of the ball is the 2D universe time is the vector normal of the ball measured in imaginary number i. So light will move at 45 degree to any vector normal. The expanding ball gets bigger because time is causing it to expand outward and this is why the universe expands because of material flying out into time. Also if you travel far enough in one direction you come back to your origin like on Earth (warped space).

Would this be an accurate model of the universe?

I recall the universe was discovered to be "flat" so how big would this ball have to be so that the fact that we haven't seen parallel lines converge at any distance can be explained away that the universe is just too big for us to observe it?David

 

[PeroK]

One of the possibilities thrown up by the theory of General Relativity is a finite closed universe, as opposed to an infinite flat universe. The current observations suggest that if the universe is closed, then it must be very large, as there is no evidence of large scale spatial curvature.

Moreover, our universe appears to have the critical matter-energy density required for an infinite flat universe:

https://en.wikipedia.org/wiki/Friedmann_equations#Density_parameter

 

[Bandersnatch]

Would this be an accurate model of the universe?

It's tempting to imagine the spherical geometry that way, but it doesn't work with time as the radial component. The scale factor does not grow linearly with cosmic time, as it would have to be doing in this scenario.

I recall the universe was discovered to be "flat" so how big would this ball have to be so that the fact that we haven't seen parallel lines converge at any distance can be explained away that the universe is just too big for us to observe it?

If you forget about including time in there, and instead treat the radius of the sphere as just the radius of its curvature, then this radius would have to be at least ~205 Gly (this comes from the error bars on the density parameter, mentioned above, as per the latest Planck data).

 

[darkdave3000]

So is there a relationship between the expansion of the universe and curvature? Change in Surface Area Vs Change in Radius? And is dark energy (expanding universe) merely caused by the passage of time?

 

[PeroK]

So is there a relationship between the expansion of the universe and curvature? Change in Surface Area Vs Change in Radius? And is dark energy (expanding universe) merely caused by the passage of time?

Everything is related by the Friedmann equation:

https://en.wikipedia.org/wiki/Friedmann_equations

The universe is a 4D manifold (three space plus one time). It's only a crude analogy to compare it to an expanding sphere in 3D space.

It's not dark energy that causes expansion; expansion is a result of the laws of GR and the Friedmann equation. Dark energy, however, is responsible for the current accelerating expansion. Without dark energy, the universe would still be expanding - but the expansion would be slowing down.