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

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Discussion Overview

The discussion revolves around expressing redshift as a function of distance modulus (DM) in the context of an empty universe model (Omega=0). Participants explore theoretical aspects of cosmology, particularly focusing on the implications of different universe models, including closed and open universes, and their relation to redshift and expansion.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant seeks a function for redshift as a function of DM in an empty universe model and mentions downloading supernova data for analysis.
  • Another participant references resources that may assist in deriving the necessary equations related to the Milne cosmology.
  • There is a contention regarding the nature of closed and open universes, with some arguing that a closed universe can still expand or shrink.
  • Participants discuss the distinction between closed universes and closed manifolds, suggesting that a closed manifold does not preclude expansion.
  • Some participants assert that the universe could be considered a closed manifold at certain points after the Big Bang, depending on mass/energy distributions.
  • There is debate over the definition of a closed manifold and its implications for the universe's expansion, with some arguing that a closed manifold is finite and cannot expand infinitely.
  • Participants discuss the concept of a manifold in general relativity, with disagreements on whether the manifold itself can change over time.
  • There is a clarification that a metric is distinct from a manifold, with metrics defining measurements within a manifold.
  • One participant emphasizes the need to distinguish between spatial and temporal infinity in cosmological models.

Areas of Agreement / Disagreement

Participants express differing views on the nature of closed and open universes, the implications of manifold definitions, and the relationship between expansion and topology. No consensus is reached on these points, and the discussion remains unresolved.

Contextual Notes

Participants reference various resources and papers, indicating that the discussion is informed by ongoing research and theoretical exploration. The conversation includes complex definitions and assumptions that may not be universally agreed upon.

  • #31
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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  • #32
Maybe time orientable is a locale property, which may not necessarily exclude the possibility of closed timelike geodesics?
 
  • #33
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.
 
  • #34
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.
 
  • #35
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.
 
  • #36
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.
 

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