keepitmoving said:
imagine the overall universe as being really big such that minor variations in the overall density of our visible universe are no more significant to the overall universe than local variations of density in our visible universe are to our overall density. The "minor" variations in the density of our visible universe would be insignificant to the really big universe. Wouldn`t this eliminate the flatness problem?
No, because the flatness problem is one that doesn't care much about what scale you look at.
Here is, in essence, the problem. If we completely ignore the fact that there are density perturbations at all, and just consider a perfectly smooth universe, then there are only a few parameters that fully describe the behavior of the system: the density of the various components, whether the universe is expanding or contracting, and the overall spatial curvature.
It is the overall spatial curvature that we're talking about when we consider the flatness problem. And it goes as follows: in order for the universe to last to current times, the overall spatial curvature must be pretty small. It can't be large and positive, because then the universe would have just recollapsed by now. It can't be large and negative, because then everything would just be moving too quickly apart and we wouldn't have any structure around. It has to be at least somewhat near zero today just for us to be here.
But here's the problem: if we take a universe dominated by normal matter, then the density of the normal matter scales as 1/a
3. But the effect of the curvature scales as 1/a
2! So as the universe expands, the matter dilutes away. The effect of the curvature dilutes away too, but it does so more slowly: a small curvature today means that the curvature had to be really really small when the universe was a fraction of the current size. For example, the CMB was emitted when the scale factor of the universe was around 1000 times smaller than it is today. That means that the effect of the curvature would have been 1000 times less compared to matter at the emission of the CMB. If, say, we can limit the curvature to +/- 10% today, then it had to be around +/- 0.01% when the CMB was emitted!
Then, what happens if we go even further back? Well, if we go far enough back, the predominant energy density of our universe was in photons, which lose energy as 1/a
4. So the problem is gets even worse. At very early times, the curvature had to be
fantastically small. And small numbers need explaining.
That, in a nutshell, is the curvature problem. And by the way, the curvature problem is solved by cosmic inflation.
keepitmoving said:
Also, imagine our universe as a virtual universe and therefore a temporary universe in a really big and long lived universe in the same sense as we have virtual particles here that are temporary.
I'm not sure what you mean.
