Master Thesis

100000
10000
1000
100
10
1
Dgγ
Dg b
Dgc
Densityperturbations
10
1
0.1
0.01
Velocityperturbations
0.1
0.001
0.01
0.0001
0.001
0.0001
1e-05
1e-07 1e-06 1e-05 0.0001 0.001 0.01 0.1 1
1e-07 1e-06 1e-05 0.0001 0.001 0.01 0.1 1
a
a
Potential
Potential nonlogarithmic
1
Ψ
Ψ
1
Φ
Φ
0.5
0.1
0
0.01
-0.5
0.001
0.0001
-1
1e-07 1e-06 1e-05 0.0001 0.001 0.01 0.1 1
1e-07 1e-06 1e-05 0.0001 0.001 0.01 0.1 1
a
a
decouple fromphotons andaredraggedintothe CDMpotential. 366.3
Figure6.2: Evolution ofthe Density, Velocity andPotentialPerturbations
The perturbation has a momentum scale of k=3.7h M pc −1 , corresponding to an extension ofλ=1.7h −1 M pc. Scale factor a is used as association of time.
Neutrino perturbation is not shown in the plots, because it would contribute only during radiation dominance, where it oscillates with the photon perturbation.
Shear isnegligibletoobecause of relation (5.35) and thelower rightplot.
The perturbation evolution behaves as described in the literature: At the beginning density and potential variables remain constant until they enter the horizon,
which happens at a(x)| 1.0= 8.3·10 −7 . Now radiation pressure forces a start of oscillations of the perturbations. These repulsive forces drive the gravitational
potential(ΦandΨ)downasshowninthelowerplots. At a=3·10 −4 theoscillationsaredampedbyphotondiffusion. Afterrecombination at a=8.8·10 −4 baryons
−Vγ
−Vb −Vc
The Evolution of Perturbations