Big Bang Shock Wave
Before considering the two questions of how a shock wave can propagate if there is no space into which to propagate and how, even if it could somehow propagate, impossibly unstable it would be, we need to look at how a supernova might appear in our flat model.
We know that all supernovas have a compressed electomagnetic wave at their leading edge. We are most familiar with the energy shock wave that lies within the visible spectrum of the electro magnetic spectrum. A super nova's spherical 'halo' or volume of influence might have a diameter of several billion light years while its 'compression' wave in the visible spectra might only be about 1/20th of a light year in thickness (a ratio of 1:40,000,000,000). Similarly, the matter that gets ejected during a supernova event can also exhibit a density wave at the leading edge.
The balance of material remaining within the halo is often somewhat randomly distributed, almost nondescript.
If you were to model the propagation of a supernova explosion using our flat universe model it's shock wave might best be represented by a ring... expanding outward.
Similarly, if you were to model the propagation of a supernova explosion using a positively curved universe model the shock wave might look like a ring propagating outward from a point. (Each sphere shown here indicating successive points in time, moving from left to right) If it were to explode at the north pole, we would expect it to propagate southward, towards the 'equator'.
If the universe's expansion is factored in and ignoring, for the moment, the relative rates of universe's expansion and the rate of propagation of the supernova explosion. The supernova's shock wave could still in this model travel into the hemisphere opposite to where it started from. (i.e. move from the north pole into the southern hemisphere)
Like someone maintaining their position relative to the loading platform by walking backward on a train as it moves out of the station, you could engineer a model such that space expanded at a rate that would exactly offset that of the supernova's propagation. If just the right balance could be struck, the supernova's shock wave would remain at a constant 'distance' (d) above the south pole, a kind of 'standing wave' as space 'moves' by.
Now consider this in the context of the big bang. The distance d would have to decrease.
In fact, with both the expansion of space and big bang shock wave commencing at time zero the distance 'd' would have to approach zero. Under this senario the black surface is really just a standing wave, at a point in space. Employing this model allows the big bang shock wave to 'propagate' relative to other points in space, simply with the expansion of the model itself. In other words, the black surface would be pushing the 'boundary' literally defining space as it grows. And secondly, because the black surface is at the same time a point in space in a positively curved universe, it is inherently stable.
Up until recently, this proposed model would have had to be ruled out on the grounds that it predicts both an inhomogeneous and anisotropic universe. All our observations until recently indicated the exact opposite, homogeneity and isotropism. If the universe truly is homogeneous and isotropic, the only way this model could possibly be correct would for us to be located exactly at the 'north' pole, a position 'furthest' from the south/black pole. The odds of this occurring would be so infinitesimally small as to make it not worth considering. With more and more evidence potentially pointing to a slightly lopsided universe, however, would mean we no longer have to occupy such a prohibitively privaledged position in the cosmos.
You often hear scientists describe a positively curved universe as being one which would allow you to see the back of your head through a telescope. This would not be possible under this model and is misleading. Observations made in any direction from any point (say the yellow dot on the diagram to the left) in this universe would be bent to travel along light paths (red dashed lines) that would end up passing into the black pole (red dot at the south pole in the diagram). The closer an observer's position in the universe to the black pole, the tighter the radius of curvature of the light paths. Observations in the 'north' and 'south' directions would travel along a great circle coincident with the two poles while observations in the 'east' and 'west' directions would have the greatest degree of 'bending'.
One of the interesting aspects of this model is that, with two thirds of the mass tied up in the black surface/black pole (red dot at the bottom), there does not appear to be any requirement for dark energy. All matter would accelerate towards the black pole under the Newtonian model. From the perspective of any observer, however, the expansion would appear outward.
The curved surface that the above model depicts is not a curve in the 3 dimensions we are familiar with. Rather it is a curve in a 4th dimension. The additional dimension provides the framework that allows our familiar 3 dimensional space to curve back in on itself (refer to 4-D animation below). Our limited 3 dimensional mind has difficulty appreciating this model but we are not limited to 3 dimensions from a mathematical perspective.
You often hear scientists describe a positively curved universe as being one which would allow you to see the back of your head through a telescope. This would not be possible under this model and is misleading. Observations made in any direction from any point (say the yellow dot on the diagram to the left) in this universe would be bent to travel along light paths (red dashed lines) that would end up passing into the black pole (red dot at the south pole in the diagram). The closer an observer's position in the universe to the black pole, the tighter the radius of curvature of the light paths. Observations in the 'north' and 'south' directions would travel along a great circle coincident with the two poles while observations in the 'east' and 'west' directions would have the greatest degree of 'bending'.
One of the interesting aspects of this model is that, with two thirds of the mass tied up in the black surface/black pole (red dot at the bottom), there does not appear to be any requirement for dark energy. All matter would accelerate towards the black pole under the Newtonian model. From the perspective of any observer, however, the expansion would appear outward.
The curved surface that the above model depicts is not a curve in the 3 dimensions we are familiar with. Rather it is a curve in a 4th dimension. The additional dimension provides the framework that allows our familiar 3 dimensional space to curve back in on itself (refer to 4-D animation below). Our limited 3 dimensional mind has difficulty appreciating this model but we are not limited to 3 dimensions from a mathematical perspective.
An observer positioned exactly at the 'north' pole would not be able to detect the black pole no matter how sophisticated the observer's equipment is. From most other positions in the universe you would also not be able to detect the black pole directly. Asymmetries would simply increase as you moved off of the 'north' pole. Observations in all directions would indicate an accelerating expanding universe with more and more red-shifting at larger distances (towards the edge of the observable universe and towards the black pole's/black surface's event horizon). It would only be as you get close to the black hole that 'distortion' of the back drop of galaxies would become observable.
As you moved closer to the black pole/black surface, like approaching any black holes event horizon, the universe would appear to turn inside out.
The 4-d animation below sometimes helps with appreciating how the universe might wrap back in on itself.
There is another interesting feature tied to the Big Bang Shock Wave in a Positively Curved Universe model. As space expands and the distance between the black pole and the balance of matter increased, the gravitational forces between the two decreased. So with time accelerations decreased. More recent measurements of increasing accelerations may mean that the extent of space has reached its zenith and has started its decent towards the big crunch.
The relationship between the models size above (how large space is) and the corresponding acceleration rates through out the last 13.82 billion years: high rates followed by decreased rates followed by increasing rates not only seems plausible under this model, but might offer an explanation of the changing value of "dark energy".
