B 2D Model of the Universe as an expanding ball

darkdave3000
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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
 
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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
 
darkdave3000 said:
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.

darkdave3000 said:
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).
 
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?
 
darkdave3000 said:
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.
 
https://en.wikipedia.org/wiki/Recombination_(cosmology) Was a matter density right after the decoupling low enough to consider the vacuum as the actual vacuum, and not the medium through which the light propagates with the speed lower than ##({\epsilon_0\mu_0})^{-1/2}##? I'm asking this in context of the calculation of the observable universe radius, where the time integral of the inverse of the scale factor is multiplied by the constant speed of light ##c##.
The formal paper is here. The Rutgers University news has published a story about an image being closely examined at their New Brunswick campus. Here is an excerpt: Computer modeling of the gravitational lens by Keeton and Eid showed that the four visible foreground galaxies causing the gravitational bending couldn’t explain the details of the five-image pattern. Only with the addition of a large, invisible mass, in this case, a dark matter halo, could the model match the observations...
Hi, I’m pretty new to cosmology and I’m trying to get my head around the Big Bang and the potential infinite extent of the universe as a whole. There’s lots of misleading info out there but this forum and a few others have helped me and I just wanted to check I have the right idea. The Big Bang was the creation of space and time. At this instant t=0 space was infinite in size but the scale factor was zero. I’m picturing it (hopefully correctly) like an excel spreadsheet with infinite...
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