How does the curvature of the universe evolve in cyclic models?

In summary: But it would make sense that they would have considered how it would have changed depending on the initial conditions.
  • #1
zeebo17
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How has the curvature of the universe changed with time?

I know that the universe is observed to nearly flat at the present time and that inflation was proposed (one of the reasons) to drive the universe to be almost perfectly flat. Do we have any idea what [tex]\Omega[/tex]k could have been like before inflation and how it changed during inflation?

Thanks!
 
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  • #2
zeebo17 said:
How has the curvature of the universe changed with time?

I know that the universe is observed to nearly flat at the present time and that inflation was proposed (one of the reasons) to drive the universe to be almost perfectly flat. Do we have any idea what [tex]\Omega[/tex]k could have been like before inflation and how it changed during inflation?

Thanks!
Basically, the curvature portion [tex]\Omega_k[/tex] changes with the energy density as [tex]1/a^2[/tex]. So if, for instance, you are matter dominated, as matter dilutes as [tex]1/a^3[/tex], as the universe expands curvature becomes more and more important. By contrast, during inflation, our universe was dominated by some stuff that acted much like a cosmological constant, which means its energy density was nearly independent of the expansion. So as the expansion progressed during inflation, the curvature diluted away as [tex]1/a^2[/tex]. As a result, we can't really know what it was before inflation began, as inflation set it to be nearly identically zero due to the massive increase in [tex]a[/tex] during that time.
 
  • #3
That remains mostly in the realm of the unknowable. Our best effort to probe beyond the surface of last scattering is WMAP. The evidence is still tenuous. If we assume the universe arose from a 'big bang', we are forced to assume something prevented it from either immediately collapsing, or expanding out of view.
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  • #4
In a one time big bang model, as noted, so far we know little if anything before inflation, as things were apparently infinite or at least our models break down there.

But in cyclic models of the universe, where the bang is finite and mathematically consistent, such information is available. One such model is the subject of a recent book: THE ENDLESS UNIVERSE, BY Paul Steinhardt and Neil Turok, 2007. I don't recall them specifically mentioning omega in the book.
 

1. What is the curvature of the universe?

The curvature of the universe is a measure of the overall shape of the universe. It is determined by the geometry of space and can be either flat, open, or closed.

2. How is the curvature of the universe measured?

The curvature of the universe is measured using observations and measurements from various astronomical tools and methods. This includes studying the cosmic microwave background radiation, analyzing the movement of galaxies, and measuring the overall density of the universe.

3. What does it mean for the universe to be flat, open, or closed?

If the universe is flat, it means that space is infinite and parallel lines will never intersect. An open universe has a negative curvature, meaning space is open and expanding. A closed universe has a positive curvature, meaning space is finite and will eventually collapse on itself.

4. What implications does the curvature of the universe have on its fate?

The curvature of the universe plays a significant role in determining the fate of the universe. A flat universe suggests that the expansion of the universe will continue forever. An open universe suggests that the expansion will continue and eventually lead to the "heat death" of the universe. A closed universe suggests that the expansion will eventually reverse and lead to a "big crunch" where the universe collapses in on itself.

5. How does the concept of dark energy affect the curvature of the universe?

The existence of dark energy, a mysterious force that is causing the universe to expand at an accelerating rate, has a significant impact on the curvature of the universe. It is believed that dark energy is the dominant force driving the expansion of the universe, and its presence suggests that the universe will continue to expand forever, regardless of its initial curvature.

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