Why is the Poincaré dodecahedron not observed in the universe?

[fmichel]

I have just listened the cosmologist Hubert Reeves on a radio broadcast.
He says that there are clusters of galaxies, superclusters of galaxies, but he also says that there are no super-superclusters of galaxies.

My question is the following: do we know why there are no super-superclusters of galaxies?

Is there an insight (not a proof of course) that the size of the universe is finite?

It seems to me that if the universe is infinite, it would exist super-superclusters, super-super-superclusters, super-super-super-superclusters and so on... like a fractal structure. There would always be a superstructure for every structure. But perhaps there are some defaults in my vision of an infinite universe.

 

[George Jones]

Even if the universe is infinite, the observable part of the universe, i.e., the part of the universe that lies on our past lightcone, is finite.

 

[EL]

My question is the following: do we know why there are no super-superclusters of galaxies?

I'm not an expert on structure formation but I can think of a simple answer:
There hasn't been enough time since the Big Bang for super-superclusters to form. Structures start out small and then grow by merging, and at this moment we're at the "age of superclusters". Wheter there will be any super-superclusters later on depends on how the expansion rate goes.

 

[russ_watters]

Even if the universe is infinite, the observable part of the universe, i.e., the part of the universe that lies on our past lightcone, is finite.

Not really my area, but in addition to not being able to see them because they are too far away/big, could they be too far away to gravitationally interact due to he finite speed of gravity?

 

[Chronos]

The lack of supercluster clusters is an observational constraint.. George's finite universe model, EL's time constraint ands Russ's finite speed of gravity all fit and make sense to me.

 

[SpaceTiger]

He says that there are clusters of galaxies, superclusters of galaxies, but he also says that there are no super-superclusters of galaxies.

It's likely that he's just referring to the largest gravitationally bound objects. There are thought to be inhomogeneities and overdensities at all scales, even those beyond the visible universe. For example, filamentary structure is often seen on scales larger than that of superclusters (depending on one's definition of the latter), but filaments are not generally bound.

My question is the following: do we know why there are no super-superclusters of galaxies?

I agree with EL's explanation.

Is there an insight (not a proof of course) that the size of the universe is finite?

The existence of a largest bound object is actually an inidication of the universe's finite age (since inflation) rather than its finite size.

It seems to me that if the universe is infinite, it would exist super-superclusters, super-super-superclusters, super-super-super-superclusters and so on... like a fractal structure.

The universe is observed to exhibit a fractal structure on intermediate scales (~tens of megaparsecs), but on the largest scales it approaches homogeneity. This is thought to be a consequence of inflation, which gives rise to a scale-invariant "primordial" spectrum of density perturbations.

There would always be a superstructure for every structure. But perhaps there are some defaults in my vision of an infinite universe.

A matter-dominated universe would grow structure on any scale if given enough time. If there really is a cosmological constant, however, we can expect the growth of structure to halt on the scale of superclusters.

 

[hurk4]

The universe is observed to exhibit a fractal structure on intermediate scales (~tens of megaparsecs), but on the largest scales it approaches homogeneity. This is thought to be a consequence of inflation, which gives rise to a scale-invariant "primordial" spectrum of density perturbations.

Is fractal structure then not a counter-argument against inflation?
kind regards.

 

[SpaceTiger]

Is fractal structure then not a counter-argument against inflation?

If the universe were fractal to arbitrary scales, then inflation would likely be incorrect. It isn't, however, and the observed power spectrum of large scale structure is so far consistent with simple inflationary models.

 

[hurk4]

If the universe were fractal to arbitrary scales, then inflation would likely be incorrect. It isn't, however, and the observed power spectrum of large scale structure is so far consistent with simple inflationary models.

Thank ST you for your clear answer.
Then this restricted fractionallity is an argument for inflation to be right?!.
On the other hand, since our observable universe is only a very smal part of our universe (which might even be a black hole. In that case only a local region around us will be homogenious and isotropic) it is thinkable, (but not proven) that the fractional character is really restricted. But I am certainly not a professional and have a great tendency to believe you. I also think that indeed phycal behaviour is scale dependent and as a consequence algorithms underlying fractals can be scale depedent so that fractality can have a begin and an end.

 

[SpaceTiger]

Then this restricted fractionallity is an argument for inflation to be right?!.

I think it's unclear at this point. Inflation gives scale-invariant initial conditions, but it's difficult`to simulate its evolution after it becomes non-linear and non-gravitational interactions become important. The fractal structure is a result of non-linear gravitational evolution (as well as some non-gravitational interactions in the baryonic component), so the precise power spectrum at small scales is not always reproduced in simulations.

On the other hand, since our observable universe is only a very smal part of our universe (which might even be a black hole).

The universe is http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/universe.html" .

I also think that indeed phycal behaviour is scale dependent and as a consequence algorithms underlying fractals can be scale depedent so that fractality can have a begin and an end.

Fractal behavior, in this case, just means that the matter distribution can be approximated by a particular power spectrum. This does not mean that the formation process followed a "fractal" algorithm.

 

[hurk4]

The universe is http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/universe.html" .

Since I feel that beginning (creation) and consequently ending are not existing I have difficulty with the article given by your link. I quote:

"The short answer is that the big bang gets away with it because it is expanding rapidly near the beginning and the rate of expansion is slowing down".

Personnaly I intuitively feel that there must be a pre-bang situation for our universe and that singularities don't exist physically.
If our observable universe could be part of an inner area of a black hole, than this kernel could be a kind of swinging thing where we only observe an expanding era. Of course the local homogeneity we observe is counterintuitive to such an idea, but if its only a very very tiny part than
one can think of it. Lifetime of such a very big black hole will be long enough to supply us with a lot of pre- and after-bang time.

 

[SpaceTiger]

Since I feel that beginning (creation) and consequently ending are not existing I have difficulty with the article given by your link. I quote:

"The short answer is that the big bang gets away with it because it is expanding rapidly near the beginning and the rate of expansion is slowing down".

Personnaly I intuitively feel that there must be a pre-bang situation for our universe and that singularities don't exist physically.

For the universe to be a black hole, there would have to be a singularity in our future. Even your "beliefs" rule out this idea.

 

[hurk4]

For the universe to be a black hole, there would have to be a singularity in our future.

Since I posted the thread "singularity or Planck-density" and the reactions I got, I became even more convinced that singularities can only exist(if the do ?) as mathematical constructs and will have nothing to do with physical reality. But, avoiding just playing with words, maybe you mean something like a domain with a very high density <= Planckdensity? But I suppose/speculate, the black hole was aready existing long before an era of expansion of its kernel begun during which something like contraction of this kernel happened. All "the dancing" happening in the inside of BH with its constant radius many many orders larger than the radius of the O.U.

Even your "beliefs" rule out this idea.

Maybe I am wrong, but being part of what ever exists I feel that intuition
is a better guide than believings. Sorry for this non-physical argument.
Kind regards

 

[SpaceTiger]

But I suppose/speculate, the black hole was aready existing long before an era of expansion of its kernel begun during which something like contraction of this kernel happened. All "the dancing" happening in the inside of BH with its constant radius many many orders larger than the radius of the O.U.

You can't put an observer inside of a black hole and have them see what we're seeing in our universe. That's the point of the link I gave. You can "modify" the black hole metric such that a small part of it is expanding, but then it's not really a black hole anymore. Furthermore, it's a really ad hoc modification. A discussion of the universe at scales much larger than we can observe may as well be philosophy.

 

[Chronos]

I concur with ST's explanation. In a 'black hole' universe, space should curve back upon itself [e.g., poincare dodecahedron's]. This is not observed. See:

A cosmic hall of mirrors
http://physicsweb.org/articles/world/18/9/3

I also affirm ST's mildly understated case that any discussion of inherently unobservable consequences outside our observable universe is metaphysics

 

[hurk4]

You can't put an observer inside of a black hole and have them see what we're seeing in our universe. That's the point of the link I gave. You can "modify" the black hole metric such that a small part of it is expanding, but then it's not really a black hole anymore. Furthermore, it's a really ad hoc modification. A discussion of the universe at scales much larger than we can observe may as well be philosophy.

I am very grateful ST that you gave your time and insight to argue with me about this item, which I agree, has a tendance to be philosophy and metaphysics. I hope I did not to much irritate you and other physisists reading my stuff . But as you probably understood I have a problem with "notions" like beginning, creation, and so on. So far physics as it went does not help me too much to proceed any further, but I am glad to see that analyzing and interpretation of e.g. cmb such as you and the WMAP team does go a direction I am happy with.
If I may, then make a last remark here.
I think that many excellent physisists are known for their aversion for philosophy and metaphysics and at the same time I think that many of those physicist are among those who really contributed to good philosophy and also that it were physisist who could transform metaphysics into good physics.

 

[hurk4]

I also affirm ST's mildly understated case that any discussion of inherently unobservable consequences outside our observable universe is metaphysics

I agree.
kind regards
Hurk4

 

[hurk4]

not so surprised

In a 'black hole' universe, space should curve back upon itself [e.g., poincare dodecahedron's]. This is not observed. See:

A cosmic hall of mirrors
http://physicsweb.org/articles/world/18/9/3

Thank you Chronos.
should?
I will take this with me on holydays in France to morrow. I will also take with me J.P. Luminet's Book L' universe chiffoné, which book I have looked through some time ago. Unfortunately I never studied topology and I don't have the excellent Escher's imagination, but intuitively I was not surprised that the dodecahaedron was not found. I admire very much Poincaré o.a. for he was a (the?) (co)founder of SR theory and for his recurrency principle (only valid for a closed system) and his basic work underlaying chaos theory.