Master Thesis

More documents

Recommendations

Info

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
Ω Λ 3 2 1 0 No Big Bang 95.4% 99.7% 68.3% Open Closed Accelerating Decelerating Expands to Infinity Recollapses ΩΛ=0 Ω tot=1 q 0=-0.5 q 0=0 q 0=0.5 -1 0.0 0.5 1.0 1.5 2.0 2.5 ΩM Figure4.2: SN1a dataat the fundamentalplane At the fundamentalplanethe parametersΩ M andΩ Λ canvary.Ω K variesalsoindirectly because of (4.76). One sees, thatΩ M≈ 0.3 andΩ Λ≈ 0.7 . (Adaptedfrom [22], Fig. 8) 4 The Homogeneous Universe 25 ^
Page 1: Structure Formation in the Universe
Page 5 and 6: Contents 1 Introduction 5 2 Equival
Page 7: 1 Introduction At high energies the
Page 10 and 11: 1. Spacetime is endowed with a symm
Page 12 and 13: One can see, that the differentials
Page 14 and 15: 3.5 The Connection 3.5.1 Geometric
Page 16 and 17: 3.7 Torsion andCurvature The Torsio
Page 18 and 19: It is an important property that th
Page 20 and 21: One concludes that the space of con
Page 22 and 23: 4.4 ScalefactorandRedshift For simp
Page 24 and 25: 4.6 The FriedmannEquations Summing
Page 28 and 29: 4.8 Inflation Inflation, first intr
Page 30 and 31: 10 1 1e+12 1e+10 1e+08 1e+06 10000
Page 32 and 33: With this metric, the velocity pert
Page 34 and 35: 5.2 InitialConditions According to
Page 36 and 37: CDM density perturbation today. Unf
Page 38 and 39: 100000 10000 1000 100 10 1 Dgγ Dg
Page 40 and 41: 10000 1000 100 10 1 0.001 0.01 k/h
Page 42 and 43: timesteps 1e+09 1e+08 1e+07 1e+06 1
Page 44 and 45: Performing on the other hand a Four
Page 46 and 47: α(Ω b,Ω c)=0.8873 andβ(Ω b,
Page 49 and 50: 8 The search for a cutoff Now the q
Page 51 and 52: 8 The searchfor a cutoff 49 ∆ 2 (
Page 53 and 54: Figure8.4: Luminosityfunction ofgal
Page 55: λ0/m Inflation aRH Radiation domin
Page 59 and 60: Descriptions Acbar: Arcminute Cosmo
Page 61 and 62: Bibliography [1] Clifford M. Will,
Page 63: [48] Simon P. Driver, Paul D. Allen

Master Thesis

Create successful ePaper yourself

Delete template?

Save as template?