- 29 Aug '16 17:26http://www.zmescience.com/research/dark-flow-leads-researchers-to-exotic-conclusion/

I had a half baked theory about what causes the expansion of the universe now, that is a bunch of universes surrounding ours like the bits of foam in pillows and such, each one attracting matter so overal it looks like expansion of the universe which it would be but just due in this case to other universes just outside our 'bubble'. - 30 Aug '16 02:20

Tell me, what piece of published research links the density of the universe to its overall shape? Spherical symmetry is assumed in things like the derivation of the Robinson-Walker metric, but the matter distribution is assumed to be uniform. The point is that if the matter density in the universe were zero then we have no good reason to believe it would be anything other than spherically symmetric. It is not the magnitude of the density, but its uniformity, that produces spherical symmetry in the observable universe. Also tell me where you get the notion that its "outer edge" would move at the speed of light? Neither of these ideas are part of the standard model of cosmology (the Lambda-CDM model).*Originally posted by apathist***If the density of our universe is great enough then it would have a spherical shape. Or so the science says. And its expanding, so the outer edge is moving at c. But that is just the outer edge to us. Pick a point on the edge and everything expands from there too.** - 30 Aug '16 07:55

Science says no such thing.*Originally posted by apathist***If the density of our universe is great enough then it would have a spherical shape. Or so the science says.**

**And its expanding, so the outer edge is moving at c.**

Again, not what science says.

**But that is just the outer edge to us. Pick a point on the edge and everything expands from there too.**

Then it isn't the edge. - 30 Aug '16 07:59

I disagree. To talk of a spherical shape at all implies edges which simply don't exist - at least I have never seen any scientific theory that suggests such a thing is possible. Now you may mean spherical in higher dimensions, but if so, then say so.*Originally posted by DeepThought***The point is that if the matter density in the universe were zero then we have no good reason to believe it would be anything other than spherically symmetric.**

The universe is either flat and infinite or curves back on itself, but not in the three dimensions but a higher dimension. In the three dimensions it has no edge. - 30 Aug '16 09:07

It seems to me there would have to be higher dimensions involved to make some kind of spherical universe and that is how I think of universes as bubbles in foam.*Originally posted by twhitehead***I disagree. To talk of a spherical shape at all implies edges which simply don't exist - at least I have never seen any scientific theory that suggests such a thing is possible. Now you may mean spherical in higher dimensions, but if so, then say so.**

The universe is either flat and infinite or curves back on itself, but not in the three dimensions but a higher dimension. In the three dimensions it has no edge. - 30 Aug '16 14:06

I was taking "spherical" to mean spherically symmetric. In fact in these metrics for the closed case one can choose coordinates where the space-like slices are three spheres. For an infinite universe I'm simply requiring a metric that is spherically symmetric. This may not be what apathist meant by "spherical", but it's the closest thing I could think of to what he said that makes any sense.*Originally posted by twhitehead***I disagree. To talk of a spherical shape at all implies edges which simply don't exist - at least I have never seen any scientific theory that suggests such a thing is possible. Now you may mean spherical in higher dimensions, but if so, then say so.**

The universe is either flat and infinite or curves back on itself, but not in the three dimensions but a higher dimension. In the three dimensions it has no edge. - 30 Aug '16 16:34

When I think of dimensions I think a higher dimension includes all instances of a lower dimension so a 2 dimensional structure would contain all instances of a 1 dimensional concept and a 3 dimensional concept would 'hold' all 2 dimensional constructs.*Originally posted by DeepThought***I was taking "spherical" to mean spherically symmetric. In fact in these metrics for the closed case one can choose coordinates where the space-like slices are three spheres. For an infinite universe I'm simply requiring a metric that is spherically symmetric. This may not be what apathist meant by "spherical", but it's the closest thing I could think of to what he said that makes any sense.**

So expanding that to 4th, 5th, 6th, etc., I would think of the higher dimensions as capable of 'holding' the lower dimensions. So not counting 4th as time but an actual dimension, I would think of that dimension as capable of 'holding' all instances of our 3 dimension space. So in that dimension there would be some limiting factor to our 3 dimension space such that it would be contained inside the 4th dimension and that space could be spherical, could be shaped like a football, or a cube, whatever, it fits in that 4 dimension space along with other 3 dimensional spaces we could never see directly but contained by that 4 dimensional space so in that reality we could have universes all around us and not know it but maybe they could interact with ours by 'bumping' into each other, leaving footprints in the CMB like we see. - 30 Aug '16 18:51

It's not obvious to me that a two dimensional flat Euclidean space (forget time for now) is capable to holding all possible one dimensional curves. To see this consider a curve on a plane embedded in the three dimensional space. Since this is Euclidean space we can choose axes so that the plane is the xy plane, in other words the set of points with z = 0. Now deform the curve so it has a bump going off the z-axis. For example for a circle around z = 0, you could have z = 0 for all x <= 0 and z = f(x) for all x > 0, with the function f(x) chosen so the curve is differentiable at least once at x = 0. Since I can always generate a higher dimensional space by translation or rotation of a lower dimensional one the only non-trivial question is what is the smallest dimensional flat space a given curved one will fit in. Given the sequence of Euclidean spaces E1, E2, E3, ... where E1 is the line, E2 the plane, E3 three dimensional space as we know it and EN is N dimensional flat Euclidean space, then for any N it is possible to find a smaller dimensional curved space that cannot be embedded in EN without losing curvature information (there's always a mapping but the resultant shape is different to the original - in my circle example the mapping would be projection onto the plane with z = 0, which misses out how the circle has been bent). You need an infinite dimensional embedding space to fit all curved spaces of a given finite dimension in.*Originally posted by sonhouse***When I think of dimensions I think a higher dimension includes all instances of a lower dimension so a 2 dimensional structure would contain all instances of a 1 dimensional concept and a 3 dimensional concept would 'hold' all 2 dimensional constructs.**

So expanding that to 4th, 5th, 6th, etc., I would think of the higher dimensions as capable of 'holding ...[text shortened]... ould interact with ours by 'bumping' into each other, leaving footprints in the CMB like we see. - 30 Aug '16 19:56

Time dilation is causing the accelerated expansion. I like your theory, but it does not explain the acceleration.*Originally posted by sonhouse***http://www.zmescience.com/research/dark-flow-leads-researchers-to-exotic-conclusion/**

I had a half baked theory about what causes the expansion of the universe now, that is a bunch of universes surrounding ours like the bits of foam in pillows and such, each one attracting matter so overal it looks like expansion of the universe which it would be but just due in this case to other universes just outside our 'bubble'. - 31 Aug '16 00:23
*Originally posted by DeepThought***Tell me, what piece of published research links the density of the universe to its overall shape?**

Here's a typical explanation. http://www.space.com/24309-shape-of-the-universe.html

**Also tell me where you get the notion that its "outer edge" would move at the speed of light?**

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

We also know that we don't have a special position in the center of our expanding universe. So my edge comment follows. - 31 Aug '16 02:25

With you now, when you say sphere you mean 3-sphere and when you say edge you mean cosmological horizon.*Originally posted by apathist**Originally posted by DeepThought*

[b]Tell me, what piece of published research links the density of the universe to its overall shape?

Here's a typical explanation. http://www.space.com/24309-shape-of-the-universe.html

**Also tell me where you get the notion that its "outer edge" would move at the speed of light?**

https://en.wikipedia. ...[text shortened]... n't have a special position in the center of our expanding universe. So my edge comment follows.[/b] - 31 Aug '16 14:56

Well, in the specifics of his post apathist started with: "If the density of our universe is great enough then it would have a spherical shape." - which I now know to translate into: "Space-like slices of the manifold in the Friedmann-Robinson-Walker model are 3-spheres if the matter density is higher than the critical density.". But "spherical shape" is pretty vague and could mean a number of things. He then talked about "its expanding, so the outer edge is moving at c", what he means was: "Its expanding so there is a cosmological horizon.", use of the words "outer edge" sounded like he thought the universe was a ball, with a literal edge, so I took his use of the word "spherical" very generally and assumed he meant any geometry with spherical symmetry. The universe, in the Friedmann-Robinson-Walker model has spherical symmetry whatever the density so I queried what he was saying.*Originally posted by twhitehead***Can you expand on that or provide a reference as I do not know what you mean (not disputing, just wanting to learn).**

The Friedmann Robinson Walker (FRW) metric is obtained on very general principles. By assuming a spatially uniform matter density, meaning the matter sector is homogenous and isotropic you can show that there are three possible space-times - one where space like slices are 3-spheres, one where they are flat and one where they are hyperbolic. All these solutions are spherically symmetric, which means the metric has a particular form, the density doesn't affect that.