How Can Redshift be Expressed as a Function of DM in an Empty Universe Model?

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George Jones said:
All compact 4-dimensional Lorentzian manifolds have closed timelike curves

A closed timelike geodesic is problematic. I’m thinking that any current spacetime manifold should be similar to a manifold near the Big Bang. Topology does not change with time.
 
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Maybe time orientable is a locale property, which may not necessarily exclude the possibility of closed timelike geodesics?
 
Imax said:
Maybe time orientable is a locale property, which may not necessarily exclude the possibility of closed timelike geodesics?
Well, the arrow of time is most likely a local property, but that doesn't make closed timelike curves any more sensible.
 
Chalnoth said:
Well, the arrow of time is most likely a local property, but that doesn't make closed timelike curves any more sensible.

If we asume that the arrow of time is a local property within a compact Lorentzian manifold, then closed timelike geodesics may be alllowed, and events could repeat.
 
Imax said:
If we asume that the arrow of time is a local property within a compact Lorentzian manifold, then closed timelike geodesics may be alllowed, and events could repeat.
Well, a compact Lorentzian manifold has closed timelike curves. That's one reason why our universe isn't one.
 
Chalnoth said:
Well, a compact Lorentzian manifold has closed timelike curves. That's one reason why our universe isn't one.

I don’t necessarily agree, but I think Aztral already go the answer he/she was looking for. What I was trying to say is that maybe there is no such thing as an empty universe. Trying to calculate properties of such a universe may be a nice exercise in mathematics or “theoretical” physics, but it may have nothing to do with reality. CMB data seems to fit better with a finite model of the universe than with an infinite model, and that seems to make sense to me.

I can see two possibilities at or near the Big Bang:

1) Space-time was infinite and somewhere within that infinite space was a very small volume (a singularity?) that contained the mass/energy of the entire universe.

2) Space-time was so badly curved (i.e. mass can bend space-time in GR) that space-time itself was finite around this volume/singularity.

My $ is on #2. Excluding possible quantum effects, topology does not change with time.