Dust filled universe but dust is a real field.

Spinnor

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Tuning the mass density of a closed dust filled universe can give us a long lived closed universe?

General Relativity can tell us how that mass density changes with time?

Instead of dust let us have a real field defined at each point of spacetime. Let us assume the field is such that in some frame the field has no momentum and only energy? Assume the energy density of the field changes with time just as the energy density of a dust filled universe. How might the amplitude (and frequency) of this field change with time so that this might happen?

Thanks for any help.
 

bcrowell

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Tuning the mass density of a closed dust filled universe can give us a long lived closed universe?
We observe that the cosmological constant is nonzero, so you can't get a closed cosmology; it's guaranteed to be open and long lived. If you're talking about a cosmology with zero cosmological constant, then this is correct.

General Relativity can tell us how that mass density changes with time?
Yes, this is what the Friedmann equations do: http://www.lightandmatter.com/html_books/genrel/ch07/ch07.html#Section7.2 [Broken]

Instead of dust let us have a real field defined at each point of spacetime.
Do you mean a real scalar field? I could be wrong, but I don't think qm even has interesting real scalar fields. To get a traveling scalar wave in qm, I think it needs to be complex.

Let us assume the field is such that in some frame the field has no momentum and only energy?
I don't think you need to add this as an extra assumption. If you're referring to the average momentum, then I think the existence of such a frame follows from homogeneity and isotropy. If you're referring to the pressure, then this is basically the definition of dust: P=0.
 
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George Jones

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We observe that the cosmological constant is nonzero, so you can't get a closed cosmology; it's guaranteed to be open and long lived.
No, with a positive (as measured) cosmological constant, there is no longer a direct correspondence between openness and infinitely long-lived expansion, i.e., it is possible to have a closed universe that expands forever. In fact, current measurements do not rule this out.
 

bcrowell

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No, with a positive (as measured) cosmological constant, there is no longer a direct correspondence between openness and infinitely long-lived expansion, i.e., it is possible to have a closed universe that expands forever. In fact, current measurements do not rule this out.
Really?? Wow, that surprises me. Thanks for the correction. Can you point me to somewhere that I can read about this? Anything on arxiv.org or livingreviews.org? What measurements are necessary in order to determine whether it's open or closed? Are you talking about the mean spatial curvature of the universe, or about a purely topological thing, like forming a piece of paper into a cylinder with zero intrinsic curvature?
 

George Jones

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Really?? Wow, that surprises me. Thanks for the correction. Can you point me to somewhere that I can read about this? Anything on arxiv.org or livingreviews.org? What measurements are necessary in order to determine whether it's open or closed?
Since the late 90s, measurements indicate: a positive cosmological constant; infinite expansion; a spatial geometry that is very near the borderline between open and closed.

Almost any GR/cosmology book published after 2000 will discuss this.

Click on figure 6 from Sean Carroll's Living Review

http://relativity.livingreviews.org/Articles/lrr-2001-1/ [Broken]

to see a summary of the supernova data from a few years ago. I think we have better data now.
Are you talking about the mean spatial curvature of the universe, or about a purely topological thing, like forming a piece of paper into a cylinder with zero intrinsic curvature?
This has to do with both spatial curvature and topology. Closed in this context means that space has positive curvature, and that space is topologically compact.
 
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George Jones: The question of the geometry... that could be an artifact of the size of the universe and our place in it. I'm sold that negative curvature hasn't existed yet in our universe, but without invoking the anthropic principle, I'm not sold on the rate of expansion or its overall geometry. Too many pieces missing from that puzzle.
 

bcrowell

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Thanks, George Jones -- the livingreviews article was very helpful!
 

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