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On Fri, 13 Dec 2002, szajtan odwieczny wrote:
As Micha$B%&(B said, it's true that the deviations from homogeneity
are
small on scales anything much bigger than the Schwarzschild horizon of a SMBH http://adjani.astro.uni.torun.pl:9673/zwicky/SuperMBH
Another problem is that in the 2D balloon, the positive fluctuations (the net) are connected in a continuous network, while the negative fluctuations (lowest density) are unconnected, separated from one another.
Why do you consider that as a problem. That's just what we observe, isn't it. Those great cosmic scale filaments extending for hundredths of Mpcs.
I probably didn't write this carefully! There is no problem with the + fluctuations being connected! The problem is that the voids are unconnected in the analogy.
In reality, the voids are connected. The very low density parts of space also form a filamentary network, connecting the lowest density points to each other.
If we start with a nice N-body simulation film, and substitute densities
rho -> 2<rho> - rho
and then put in the same colour pattern for the new densities, it should look on average similar to before, at least at low density thresholds and early times.
(There is a difference on very high densities, at late times - "non-linear scales" - once there are densities greater than 2<rho>, it is clear that there cannot be perfect symmetry between + and - fluctuations.)
In the standard (3D) model, at early times the + and - fluctuations are typically of the same typical sizes (e.g. from the hypothesis of "gaussian fluctuations"), and the 2D topology of contours of constant density ("genus analysis") is connected both for + and - fluctns.
agreed but in time the curvature evolves, like everything else in this Universe. In time, because of gravity, matter tends to gather in a strings or clumps of higher density, and thus the curvature changes.
OK, fine.
If you consider all matter more dense than some value,
- a low density value gives a "gruyere (ser) topology"
- a critical density values gives a "sponge topology"
what is the difference between these two ?
between all three:
gruyere: high density regions connected; low density UNconnected sponge: high density regions connected; low density connected meatball: high density regions UNconnected; low density connected
is it only about the thickness of strings ?
- a high density gives a "meatball topology"
This is impossible to do with a balloon, which is 2D, since the topology of constant density "1-surfaces" is 1D.
Let's consider a cross section of a large part of the universe with a plain.
"plane"
Then we take a pencil and draw all the contours of a constant matter density (= constant curvature) on that plane. We make a little step back to see the picture. We will see some distinctive pattern similar to the one observed for clusters of galaxies. This is the analogy to that net on the balloon. But strings of the net are not 1D but 2D (they have width) and in reality 3D, so for the fishing net we should sometimes even fill up some gaps not allowing the balloon the out stand. This I should call now a military masking net. The constraint of 2D balloon is as you mentioned that
- fluctuations are separated. That's right but this is only because that on
2d surface a circle splits it into two regions. So in general this is not a
Agreed.
good model. In 3D we can easily jump from one loop into another, unless there are walls (also those from that masking net :) but in 3D) - like The Great Wall.
OK.
BTW, sometimes people get confused between this sort of topology (topology of 2D surfaces of constant density) and 3D topology of comoving space. Including some cosmologists like Richard Gott III who have published on both subjects ;).
na razie boud