Master Thesis

4.7.1 Values ofthedensityparameters
There are several methods for obtaining the density parameters:
1. Supernovaeoftype 1A: This method measures the redshift and distance of distant comoving objects and fits the data
through the Friedmann equation (4.77). The distant comoving objects are Supernovae 1a (SN 1a) in astronomy
(lhs of fig. 4.1).
2. The cosmicmicrowavebackgroundradiation: The small temperature fluctuations∆T of the CMB can be decomposed
into spherical harmonics and their amplitudes in dependence of l are investigated:
a lm=
�
∆T(Θ,Φ)Y lm(Θ,Φ)dΩ , δT(l)=〈|a lm| 2 〉=
�m=l
m=−l
|a lm| 2 , (4.80)
which is shown in the right-hand side figure 4.1. The first peak of this power spectrum is very sensitive to the
curvature densityΩ K, where the second and third peaks are sensitive to the contributions of the baryon- and dark
matter densityΩ b,Ω c.
3. Baryonicacoustic oscillations: In the early universe the density fluctuations of dark matter generate a gravitational
potential, in which the baryonic matter performs acoustic oscillations. These oscillations depend on the density
parameters too. Today they are manifested in the galaxy power spectrum.
4. Clustering This method is a direct measurement of the matter density. It is done by obtaining the velocity distribution
of galaxy clusters, from which the whole gravitating mass can be determined. Using this method one obtains
Ω M≈ 0.3
∆(m-M) (mag)
∆(m-M) (mag)
1.0
0.5
0.0
-0.5
-1.0
0.5
0.0
-0.5
Ground Discovered
HST Discovered
Empty (Ω=0)
Ω M=0.27, Ω Λ=0.73
"replenishing" gray Dust
high-z gray dust (+Ω M=1.0)
Ω M=1.0, Ω Λ=0.0
Evolution ~ z, (+Ω M=1.0)
0.0 0.5 1.0 1.5 2.0
z
Figure4.1: Left: Redshift of SN1a,Right: Sphericalharmoniccontributionsof the CMB
The left figure shows the distance modulus in dependence of the redshift. The dots are supernovae of type
1a. The redshift dependence of some density parameters is also plotted. The universe withΩ M = 0.27 and
Ω Λ= 0.73 ispreferred. (Adaptedfrom [22], Fig. 7)
On the right, the amplitudeδT(l) of the sphericalharmonics (4.80) is plotted over the multipole moment l. The
Acbar, Boomerang and CBI data are radioastronomy and the WMAP data comes from a satellite. The maxima
of the amplitudes get changed in their intensity and location, ifΩ M andΩ Λ are modified. Thus one can fit the
density parameterstothe CMB. (The figureistaken fromthe WMAP homepage.)
The density parameters are usually mapped in the fundamental plane of cosmology (figure 4.2).
24 4.7 Density Parameters