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

In summary: The manifold we normally talk about in GR includes both space and time dimensions. I wouldn't refer to it as changing over time. There aren't different manifolds at different times. You could take the 4-dimensional manifold-with-metric that represents a cosmological solution and make a spacelike slice through it to form a 3-dimensional manifold, but that wouldn't be "the" manifold.
  • #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.
 
<h2> What is an empty universe calculation?</h2><p>An empty universe calculation is a mathematical model used to estimate the total number of galaxies, stars, and planets in the observable universe, assuming that the universe is completely empty except for these objects.</p><h2> How is an empty universe calculation performed?</h2><p>An empty universe calculation involves using data from telescopes and other astronomical instruments to estimate the average number of galaxies, stars, and planets in a given volume of space. This data is then extrapolated to estimate the total number of objects in the entire observable universe.</p><h2> What are the limitations of an empty universe calculation?</h2><p>An empty universe calculation is based on certain assumptions and extrapolations, so it is not a precise measurement. It also does not take into account the possibility of unknown or undetected objects in the universe.</p><h2> What is the current estimate for the number of galaxies in the observable universe?</h2><p>The most recent estimate for the number of galaxies in the observable universe is around 2 trillion, based on data from the Hubble Space Telescope and other telescopes.</p><h2> How does an empty universe calculation contribute to our understanding of the universe?</h2><p>An empty universe calculation is one way to estimate the vastness and complexity of the universe. It helps us to comprehend the sheer number of galaxies, stars, and planets that exist in our observable universe, and how much we have yet to discover about the universe as a whole.</p>

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

What is an empty universe calculation?

An empty universe calculation is a mathematical model used to estimate the total number of galaxies, stars, and planets in the observable universe, assuming that the universe is completely empty except for these objects.

How is an empty universe calculation performed?

An empty universe calculation involves using data from telescopes and other astronomical instruments to estimate the average number of galaxies, stars, and planets in a given volume of space. This data is then extrapolated to estimate the total number of objects in the entire observable universe.

What are the limitations of an empty universe calculation?

An empty universe calculation is based on certain assumptions and extrapolations, so it is not a precise measurement. It also does not take into account the possibility of unknown or undetected objects in the universe.

What is the current estimate for the number of galaxies in the observable universe?

The most recent estimate for the number of galaxies in the observable universe is around 2 trillion, based on data from the Hubble Space Telescope and other telescopes.

How does an empty universe calculation contribute to our understanding of the universe?

An empty universe calculation is one way to estimate the vastness and complexity of the universe. It helps us to comprehend the sheer number of galaxies, stars, and planets that exist in our observable universe, and how much we have yet to discover about the universe as a whole.

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