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da_willem
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Does the metric of the Friedmann model yield an unbouded universe? I mean, are the geodesics of this metric closed?
pervect said:... it appears that the universe is right at the critical value. This is currently explained as a result of inflation...
Wallace said:...Inflation is a physical model that makes a prediction that [tex]\Omega = 1[/tex]...
marcus said:But the main thing I am unsure about, Wallace, is how do you get that inflation (all inflation scenarios) PREDICT that Omega must be EXACTLY equal to 1.
I was under the impression that inflation could provide one possible explanation for why Omega is either one or very very very near one.
How does it work that inflation predicts that Omega has to be exactly 1?
Wallace said:...Since inflation increases R by many times, any curvature term is beaten down to an insignificant level.
...
Wallace said:...
BTW, could you give a brief description of how 'QG bounce' solves the horizon problem? I know essentially nothing about this theory so a from the basic description would be nice.
pervect said:If you do a websearch, you should find mention of a "ciritical density" for the Freidmann universes. If the density is above the ciritical value, the universe is closed. Above the critical value, it's open. Interestingly enough, it appears that the universe is right at the critical value. This is currently explained as a result of inflation. Look up "flatness oldness problem" for more (advanced) detail.
da_willem said:But open and closed are something different than unbounded and bounded, right?! I know that open and closed versions are possible, depending on the energy content. But I was actually wondering wether an unbounded universe is possible, i.e. with closed geodesics that end on themselves
Chris Hillman said:Hi, da willem,
Looks like others gave you some good basic information about FRW models, but for more advanced students there is another issue: the local versus global distinction. All FRW models possesses a unique family of spatial hyperslices which are everywhere orthogonal to the world lines of the matter (pressureless perfect fluid or "dust" for "matter dominated" and "radiation fluid" for "radiation dominated"). But it is perfectly possible to write down models in which these slices are each constant negative curvature but compact Riemannian three-manifolds. The easiest way to see why is to read about tilings of the hyperbolic plane and to identify edges of a tile to form a "compact quotient manifold" of H^2. This point was overlooked in classic textbooks (including MTW!) and was only emphasized rather recently by Jeffrey Weeks and Neil Cornish.
marcus said:Yes! this is how I remembered it, for example as explained in Lineweaver 2003 article!
Curvature is beaten down to an "insignificant level" but not forced to be exactly zero.
SpaceTiger said:...
I haven't heard anyone making noise about the flatness assumption of late. ...
marcus said:I'm unsure about a couple of things.
I'm not sure inflation happened, now that we don't need it to solve the horizon problem (QG bounce seems to take care of different parts of the sky having roughly the same CMB temp).
hurk4 said:Nor do I.
To me, as I hesitate to say, it seems that the horizon problem and its solution (inflation) were invented as an attempt to save the idea of a beginning of the BB.
As a non professional even I myself can calculate that our observable universe compressed to Planck-density had a dimension of about 10E-12 m (taking into account 10E-87 baryons + DM + DE). This distance is by far not enough to allow communication between opposite points during Planck-time (10E-43s).
pervect said:You can find an explanation in http://www.astro.ucla.edu/~wright/cosmo_03.htm
http://www.astro.ucla.edu/~wright/cosmo_04.htm
Basically, Planck time has nothing to do with the problem.
Observations have determined that the galaxies are spread out as if they are on the surface of soap bubbles.When man discovered the soap bubbles the "inflaton" committed hari-kari.
jal said:I've been asked to expand on my comment.
It seems that I'm agreeing with most of what is being said by others in this thread.
INFLATON
Observations have determined that the galaxies are spread out as if they are on the surface of soap bubbles.
Let’s look at what gravity would be doing.
Now, let’s see what the inflaton has got to do.
The “math kids” have rendered their verdict …. They cannot make a model because of the curvature that has been created by gravity.
Gravity is not the same everywhere and the inflaton cannot act uniformly everywhere. If the inflaton existed there would be observable differences in the expansion rate which we do not see. I assumed that the papers referred in this thread are sufficient references.
pervect
If we take a large enough sphere, non-uniformities such as the voids should average out if we assume the cosmological principle holds.
I don't like to argue. I'll just listen and read any new evidence that is presented.jal
I was willing to accept it for the dust bag model. However, I was told that the galaxies are spread out on “bubbles” and it no longer works.
If you want to keep the inflaton as a mechanism then you will be going against what the observations are telling us.
The Friedmann model 'unbounded' is a cosmological model that describes the expansion of the universe. It is based on the theory of general relativity and was developed by physicist Alexander Friedmann in the 1920s.
The Friedmann model 'unbounded' differs from other cosmological models in that it assumes the universe is spatially infinite and has no boundaries or edges. This is in contrast to other models, such as the Friedmann model 'closed', which assumes a finite universe with a spherical shape.
The unbounded aspect of the Friedmann model has significant implications for the expansion of the universe. It suggests that the universe has no center and no edge, and that it is expanding uniformly in all directions.
The unbounded aspect of the Friedmann model challenges our traditional understanding of the universe as a finite and contained entity. It suggests that the universe is much larger and more complex than we previously thought, and that it may continue to expand indefinitely.
Yes, there is observational evidence that supports the unbounded aspect of the Friedmann model. For example, the cosmic microwave background radiation, which is a remnant of the early universe, appears to be uniform in all directions, indicating a spatially infinite universe. Additionally, the large-scale structure of the universe, such as the distribution of galaxies, also supports the idea of an unbounded universe.