A topological question

**ryokan** · Dec20-04, 11:47 AM

The critical density determines the Universe evolution along time. So, by measuring this density, we could know about the finite or infinite age of the Universe.

But we don't know from General Relativity if our Universe is spatially finite or infinite.

As far as I know, such question could be only answered from Topology.

If so, are there enough observational evidences to sustain any topology?

What would be the observational keys to elucidate this topology?

**Garth** · Dec20-04, 12:27 PM

If repeated patterns, "circles in the sky", were to be found in the CMB radiation that would be evidence of a closed universe.

Actually we don't even know the future of the universe by simply measuring its density. That would have been true in a plain Friedmann universe, without a cosmological constant or dark energy, but as today it is generally accepted that the universe is accelerating in its expansion and that acceleration (due to dark energy?) switches itself on and off, nothing can be said about the future. Big crunch, Big sigh, big rip????

**Chronos** · Dec20-04, 05:09 PM

If I may expand on what Garth said, repeating patterns in the cosmic microwave background [CMB] would be evidence the universe is finite, which is to say it wraps around on itself [something akin to seeing the back of your head through a telescope]. Scientists have looked for evidence of this in the CMB and came up empty. For details see
"The universe is at least 156 billion light-years wide."
http://www.space.com/scienceastronom...ay_040524.html
For a general discussion of topology and means to detect see:
Cosmic Topology: a Brief Overview
http://arxiv.org/abs/astro-ph/0402324

**meteor** · Dec20-04, 06:16 PM

There was some months ago a proposition by some people that the Universe could have the shape of a horn, a horn of finite volume. This kind of universe, called Picard Universe, is explored in this paper that has appeared this month
http://arxiv.org/abs/astro-ph/0412407
Can one hear the shape of the Universe?

**Garth** · Dec20-04, 07:11 PM

A horn? Try a cone, not only is it spatially finite, and so explains the large angle anisotopry deficiency but if of a large enough size would not necessarily show any detectable "circles in the sky", and is conformally flat, so it would be concordant with all the major WMAP features.

Garth

**Chronos** · Dec21-04, 02:41 AM

Originally Posted by Garth

A horn? Try a cone, not only is it spatially finite, and so explains the large angle anisotopry deficiency but if of a large enough size would not necessarily show any detectable "circles in the sky", and is conformally flat, so it would be concordant with all the major WMAP features.

Agreed, although I think the jury is still out on the large scale anisotropy deficiency. It does not necessarily mean the universe is spatially finite. The universe is, however, observationally finite. I therefore suspect observational evidence will indicate it is exactly as large as it appears to be.

**meteor** · Dec22-04, 01:12 AM

Try a cone...

If we are going to talk about geometry, we can also mention the Poincare dodecahedron
http://arxiv.org/abs/astro-ph/0412569

I find enticing the finite topologies. The concordance model says that the universe is infinite, but infinites are strange things. You can barely deal with them in maths... Why should them exist in real life...?

**Garth** · Dec22-04, 01:15 PM

I thought the Poincare dodecahedron has now been eliminated?
From NewScientist, 11 October 2003 "Does the universe go on forever?"

According to Weeks, the WMAP results point to a very specific illusion - that our universe seems like an endlessly repeating set of dodecahedrons, football-like shapes with a surface of 12 identical pentagons. If you exit the football through one pentagon, you re-enter the same region through the opposite face and you keep meeting the same galaxies over and over again (see Graphic). Weeks says the match between the predictions of his repeating-football model and the WMAP observations is striking ....................However, in response to Weeks's report, Spergel and his colleagues have announced evidence that contradicts the findings. They showed previously that if the universe does produce a hall-of-mirrors effect, it should be possible to find a pattern of matching circles in the microwave background around which the fluctuations are identical (New Scientist, 19 September 1998, p 28). Weeks's theory predicts six specific pairs of matching circles in the sky, but Spergel's team has had no luck finding them in WMAP data.

Garth

**ryokan** · Dec28-04, 02:36 PM

Originally Posted by Garth

If repeated patterns, "circles in the sky", were to be found in the CMB radiation that would be evidence of a closed universe.

But our universe could be also multiply-connected in absence of circles in the sky if the "cell" size were higher than our observable (horizon) universe. Is that o.k? If so, we couldn't know its topology.

And... what do you think about the possibilities of repeated patterns in distribution of quasars (or other 3D distribution) as a method to solve topology ?

**Garth** · Dec28-04, 06:08 PM

Originally Posted by ryokan

But our universe could be also multiply-connected in absence of circles in the sky if the "cell" size were higher than our observable (horizon) universe. Is that o.k? If so, we couldn't know its topology.

True

Originally Posted by ryokan

And... what do you think about the possibilities of repeated patterns in distribution of quasars (or other 3D distribution) as a method to solve topology ?

In the absence of such repeated patterns in the sky it might seem a little extravagant to invoke multiple-connected topologies, when a simply connected cone - the freely coasting closed universe - would do just as well.

Garth

[Note: the cone topology would be closed yet conformally flat and so it would be one way of explaining the WMAP data]

**Chronos** · Dec29-04, 02:28 AM

Originally Posted by ryokan

But our universe could be also multiply-connected in absence of circles in the sky if the "cell" size were higher than our observable (horizon) universe. Is that o.k? If so, we couldn't know its topology.

And... what do you think about the possibilities of repeated patterns in distribution of quasars (or other 3D distribution) as a method to solve topology ?

That is pure balogna. Show a single pattern that defies probability. Your turn. I said it does not exist, you said it did. Prove me wrong. That is a bunch of crap.

**ryokan** · Dec29-04, 07:39 AM

Originally Posted by Chronos

That is pure balogna. Show a single pattern that defies probability. Your turn. I said it does not exist, you said it did. Prove me wrong. That is a bunch of crap.

In my last post, I only posed two questions. I didn't any affirmation as you seems suggest with your "elegant" reply.

Now, I ask you these other questions:

1. Do you really think that your answer is scientific? Are terms as "balogna" and "bunch of crap" solid arguments?

2. Do you think that your answer is respectful?

I believed that this forum was scientific and respectful. With your "answer" you show me that I was mistaken.

Best wishes.

**Phobos** · Jan13-05, 01:40 PM

Chronos - That response was inappropriate. Keep the discussion civil.

Given that this thread has been inactive for 2 weeks, I'm locking it up rather than restarting any arguments.