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Cosmic Microwave Background and determination of cosmological parameters

表紙. Cosmic Microwave Background and determination of cosmological parameters. 全天マップ１. Full sky map of microwave background radiation #1. T =2.725K Cosmic Microwave Background CMB. 一様等方宇宙. Hubble parameter. Density parameter. cosmological constant (dark energy).

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Cosmic Microwave Background and determination of cosmological parameters

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  1. 表紙

  2. Cosmic Microwave Background and determination of cosmological parameters

  3. 全天マップ１ Full sky map of microwave background radiation #1 T=2.725K Cosmic Microwave Background CMB

  4. 一様等方宇宙 Hubble parameter Density parameter cosmological constant (dark energy) Standard Inflation predicts with high accuracy. The Universe is globally isotropic and homogeneous Scale factor Curvature

  5. 1022m 1012m cluster 階層 1020m Solar system galaxy 107m 1024m 1m Earth supercluster Hierarchical Structures of the Universe

  6. Large-Scale Structures Present Power Spectrum Power Spectrum of Initial Fluctuation Anisotropies in cosmic microwave background Angular Power Spectrum Hierarchical Structures in the present Universe grew out of linear perturbations under the gravity Linear perturbation Potential fluctuation Curvature fluctuation Cosmological Parameters H, W, L,...

  7. Full sky map of microwave background radiation #2 COBE COsmic Background Explorer 1993 WMAP Wilkinson Microwave Anisotropy Probe 2003

  8. WMAP 2001/6/30 2002/4: first full-sky map 2002/10: second map 2001/7/30 2001/10/1 size 5m、weight 840kg

  9. COBEのbeam widthは７度だった。

  10. Full Sky Map of Cosmic Microwave Background Radiation -200 T(μK) +200 Temperature fluctuation is Gaussian distributed. Power spectrum determines the statistical distribution.

  11. Two dimensional angular quantities: Spherical harmonics expansion Angular scaleθ: Angular Power Spectrum： Angular Correlation Function： Three dimensional spatial quantities: Fourier expansion Length scale r: Power Spectrum： Correlation Function：

  12. Before WMAP After WMAP So many data points!

  13. Cosmological Parameters beofore WMAP • Luminosity density and average M/L of galaxies • Cluster baryon fraction from X-ray emissivity and baryon density from primordial nucleosynthesis • Shape parameter of the transfer function of CDM scenario of structure formation • Many others

  14. log(dL) z Cosmological Parameters beofore WMAP • Type Ia Supernovae m-z relation

  15. Cosmological Parameters beofore WMAP SNIa+CMB +Matter density

  16. Hubble parameter was determined by HST key project. HST Key Project • CepheidsH0=75±10km/s/Mpc • SNIa H0=71±2(stat)±6(syst)km/s/Mpc • Tully-Fisher H0=71±3±7km/s/Mpc • Surface Brightness Fluctuation H0=70±5±6km/s/Mpc • SNII H0=72±9±7km/s/Mpc • Fundamental Plane of Elliptical Galaxies H0=82±6±9km/s/Mpc SummaryH0=72±8km/s/Mpc (Freedman et al ApJ 553(2001)47)

  17. H0=72±8km/s/Mpc, centered around Observation: from globular cluster from cosmological nuclear chronology Cosmological Parameters beofore WMAP Concordance Model as predicted by Inflation Cosmic age

  18. Cosmological Parameters with ERROR BARS 1st year result Concordance Model was confirmed with high accuracy. (with the help of the HST value of Hubble parameter.)

  19. ΛCDM model fits the overall feature of the angular power spectrum 6 Parameters Normalization of Fluctuations Spectral index Baryon density Dark matter density Cosmological Constant Hubble parameter in Spatially Flat Universe 899 data points are fit. Approximately scale-invariant spectrum, which is predicted by standard inflation models, fits the data. But we may also find several interesting features beyond a simple power-law spectrum…

  20. 表紙

  21. We consider temperature fluctuation averaged over photon energy in Fourier and multipole spaces. h :conformal time direction vector of photon Physics of CMB anisotropy The Boltzmann equation for photon distribution in a perturbed spacetime Collision term due to the Thomson scattering free electron density

  22. conformal time Euler equation for baryons Metric perturbation generated during inflation :Poisson equation Boltzmann eq. can be transformed to an integral equation. directionally averaged Boltzmann equation collision term Baryon (electron) velocity

  23. If we treat the decoupling to occur instantaneously at , no scattering many scattering 1 Visibility function now Last scattering surface Propagation Optical depth

  24. Integrated Sachs- Wolfe effect Observable quantity on Last scattering surface small scale ： Temperature fluctuations ：Doppler effect ：Gravitational Redshift Sachs-Wolfe effect Large scale They can be calculated from the Boltzman/Euler/Poisson eqs., if the initial condition of F (k,ti)and cosmological parameters are given. In reality, decoupling requires finite time and the LSS has a finite thickness. Short-wave fluctuations that oscillate many times during it damped by a factor with corresponding to 0.1deg.

  25. Behavior of photon-baryon fluid in the tight coupling regime Small scales：　　　　　　　　below sound horizon (Jeans scale) Oscillatory 　 （　　　　　　 is the sound speed.） Large scales：　　　　　　　 Specifically they are given by the solution of the following eqn. source term is given by metric perturbation. Initial condition of is also given by generated during inflation (if adiabatic fluc.) Inflation We need to calculate and at the Last scattering surface when photons and baryons are decoupled.

  26. r LSS d Θ～π/l Observer 図のような幾何学的関係からフーリエ空間の量がmultipole 　空間 の角度パワースペクトル　　に関係づけられる。 Fourier modes are related with angular multipoles as depicted in the figure. ～２π/k l～kdにピーク

  27. Sound horizon at LSS corresponds to about 1 degree, which explains the location of the peak 小スケールで振動 Gravitational 一般相対論的 重力赤方偏移 流体力学的揺らぎ 大スケールで ほぼ一定 hydorodynamical

  28. The shape of the angular power spectrum depends on （spectral indexetc）as well as the values of cosmological parameters. （　　　　　corresponds to the scale- invariant primordial fluctuasion.） Increasing baryon density relatively lowers radiation pressure, which results in higher peak. Decreasing Ω（open Universe）makes opening angle smaller so that the multipole l at the peak is shifted to a larger value. Smaller Hubble parameter means more distant LSS with enhanced early ISW effect. Λalso makes LSS more distant, shifting the peak toward right with enhanced Late ISW effect.

  29. Thick line 0.05 0.03 0.01 1 0.5 0.3 Old standard CDM model. 0.7 0.3 0 0.3 0.5 0.7

  30. 7 year WMAP results

  31. Tensor-to-scalar ratio vs scalar spectral index

  32. Fundamental Questions What is dark matter ? What is dark energy ? How inflation occurred ? What were there before inflation ? are yet to be answered!

  33. 表紙

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