Problem #1 [Structure Formation I: Radiation Era]

(b). How does the growth of pertubations depend on Ω 0,m ?
We can see that the growth of the fluctuations depend very strongly with Ω 0,m .
For Ω 0,m = 0.01 We can see that the growth of structure decreases very rapidly as z → 0, where
the slope of the curve aproaches 0 today. This seems very unlikely, due to the fact that we
live in a universe filled with galaxies.
For Ω 0,m = 0.10 we can see that increasing the mass density by one order of magnitude, causes
the growth of structure to continue as z → 0 and we can see that the more matter you put
into the universe the longer the growth of the fluctuations (over densities).
For Ω 0,m = 0.30 we can see that this is very similar to the last curve, except that we can see
now that it is approaching δ + m ∝ a.
For Ω 0,m = 1.00 we can see that the growth of structure is a constant
If the four models you plotted all produce the same level of pertubations today (that matches
the observed number density of galaxies, for example), how do you expect (qualitatively) the
amount of structures to differ in the four models at redshift z = 3?
To try to understand this question we can make the same plot as before, except that we must
normalize all the models to a(θ) = 1.00
1.000
δ m
+
vs a
0.100
δ m
+
(θ)
0.010
Ω m
0.001
0.001 0.010 0.100 1.000
a(θ)
thus from this plot we can see that at z = 3 the pertubations must have grown a lot faster in
the past for Ω 0,m < 1, with increasing growth as Ω 0,m → 0. This must have happened in order
for us to see the structures we see today.
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