is the universe unbounded?

[devrimci_kürt]

is there evidence its unbounded ?

 

what is difference between infinite and unbounded

 

in turkish:

infinite:sonsuz/sınırsız

unbounded:sonsuz/sınırsız :D:D unfortunately , same translation:D

 

could you give me some examples ?

[Martin]

excellent question! You ask what is the difference, and you ask for examples.

 

I think you know that cosmology is a mathematical science. It is not a verbal science, based on everyday-language words.

 

In cosmology, space is represented by a mathematical object called a differential manifold. Spacetime is also represented by a d.m.

 

An example of a d.m. could be a ring. I mean a ring which is completely alone, not part of some other figure or higher-dimension manifold.

 

Another example of a d.m. could be an infinite line, or a plane, or the traditional Euclid 3D space. These are differential manifolds.

 

Another example of a d.m. is a sphere----I mean the 2D sphere---and in particular it has no surroundings. It is alone and not in contact with any environment or higher dimensional manifold.

 

Any of these d.m. can be given a metric, or distance function. Without some metric they are formless, like a limp shapeless thing. Chosing a metric gives the d.m. some intrinsic form. Creatures moving around in it, as their universe, would be able to define and detect curvature, by measuring distances, even though there is no higher dimensional surrounding.

 

The manifold, and the metric manifold, were invented as mathematical objects around 1850, mostly at Göttingen, and they completely changed the way scientists think of space. General Relativity invented in 1915 makes the d.m. the basis, the key ingredient. And the gravitational field in that theory is actually metric itself!

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Because GR and cosmology are mathematical science, using math models instead of purely verbal concepts, people who try to think only in words about cosmology run the risk of confusion.

 

Indeed as everyday words, infinite and unbounded mean the same! So let's temporarily invent a new word: boundaryless. Meaning has no edge or boundary.

 

For example the ring universe---all existence is in this ring. This universe has no boundary. But it can have finite volume (for the one-dimensional creatures living in the ring, volume for them is 1 dimensional, we would call it length.)

 

Or the 2D sphere universe. It has no boundary, but it is also finite from the standpoint of any 2D creatures who might live there.

 

In studying d.m. all the basic concepts are defined from the inside. All the basic geometric properties are intrinsic.

 

So finiteness and edgelessness are intrinsic to be discovered by hypothetical inhabitants moving around and measuring their world with no outside reference.

 

Have I given enough examples? I think you can think of examples of other cases. Something can have a boundary and yet be infinite---like an infinite line from 0 to forever. All the non-negative numbers. It has one boundary point, which is zero. So it is bounded and also infinite.

 

Everyday language will always mess people up. In everyday language bounded = finite and unbounded = infinite. But in physical reality that is simply not true!

 

Something that is finite volume CAN have a boundary, but it also may not have a boundary. One has examples of both.

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Now you also asked "is there evidence it [the universe] is unbounded?"

 

There is rather good evidence that space is nearly flat and very large.

At the present time there is no evidence that the volume is finite, and there is no evidence that it is infinite.

If one accepts the current best-fit model (socalled LCDM) then

one can put a 95% confidence lower bound on the volume and say that it is at least 20 x 10⁶ x 10²⁷ cubic lightyears.

 

So I guess the simple answer to your question is NO. There is no evidence that the volume of space is infinite.

 

It is a convenient simplifying assumption to make but there is no evidence that it is infinite and not merely finite but very large.

Edited January 14, 2009 by Martin

[devrimci_kürt]

ok..

If universe is closed and finite, then it was born with zero volume and grew from that..

is it true?

[Martin]

ok..

If universe is closed and finite, then it was born with zero volume and grew from that..

is it true?

 

Please read the essay titled A Tale of Two Big Bangs at the Einstein Online site.

 

You are asking about something in conventional standard cosmology.

It is a common misconception that the usual BB model describes a zero volume state at the exact beginning of expansion.

 

There is also no scientific evidence that this was the beginning of the universe--that the universe was born at that point (or any other point).

 

All the model lets you do is work back to states of extremely high density.

 

Cosmologists do not agree that a singularity ever existed---a state of infinite density---they simply use the imagined singularity as a convenient time-marker, a "t = 0" reference moment.

 

The Einstein Online page describes this in more detail. The link is down at the bottom of this post.

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Kürt, I am curious about what you mean by "closed". Since 1998, a model can be spatially closed but expand endlessly (closed but no big crunch).

Before 1998 people often talked as if closed meant not only spatially closed but also headed for an eventual crunch. It is still a common misconception. Just want to be sure we understand each other about this.

 

=========================

 

If universe is spatially finite, then it is true that around the start of expansion it was spatially finite, and much much smaller.

That seems pretty obvious. The question is how much smaller!

 

It doesn't make sense to say it was infinitely small, a mathematical point, with no volume at all.

 

So smaller by what ratio? That depends on the model. It has to be a quantum cosmology (QC) model because they are the ones that succeed in getting back past the t=0 mark without breaking down. They show a bounce instead of a singularity. So there is a highest density achieved. Typically in those models the highest density is a few percent of Planck (if you know Planck units). At the most it is 40% Planck.

 

Roughly speaking this is higher than the presentday density of the universe by a factor of about 10¹²⁰.

 

At a minimum, according to 2008 WMAP data, the volume of the universe is at least 2x10³⁴ cubic lightyears. It could be much more or even infinite, but the 95% confidence interval would put it at least that.

 

So very very roughly we divide that size by 10¹²⁰ and we get the size at the time of the bounce, at the beginning of expansion, in the context of the models in question.

2x10^-86 cubic lightyear

 

If you put this into google and press search it will calculate it for you in cubic meter terms. You put in

2*10^(-86) cubic lightyear

and it will come out with something like 1.7*10^(-38) cubic meter.

Edited January 15, 2009 by Martin