1. 表紙

3. 全天マップ１ T=2.725K Cosmic Microwave Background CMB

4. Scale factor Curvature 一様等方宇宙 Standard Inflation predicts with high accuracy. Hubble parameter Density parameter cosmological constant (dark energy)

5. 階層 10 24 m 10 22 m 10 20 m 10 12 m 10 7 m 1m Earth Solar system galaxy cluster supercluster

6. grew out of linear perturbations under the gravity Potential fluctuation Curvature fluctuation CosmologicalParametersH,  Power Spectrum of Initial Fluctuation Anisotropies in cosmic microwave background Large-Scale Structures Present Power Spectrum Angular Power Spectrum Linear perturbation

7. COBE COsmic Background Explorer 1993 WMAP Wilkinson Microwave Anisotropy Probe 2003

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

9. COBE の beam width は７度だった。

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

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

12. So many data points!

13. 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. Type Ia Supernovae m-z relation log(d L ) z

15. SNIa+CMB +Matter density

16. Cepheids H 0 =75 ± 10km/s/Mpc SNIa H 0 =71±2(stat) ± 6(syst)km/s/Mpc Tully-Fisher H 0 =71±3 ± 7km/s/Mpc Surface Brightness Fluctuation H 0 =70±5 ± 6km/s/Mpc SNII H 0 =72±9 ± 7km/s/Mpc Fundamental Plane of Elliptical Galaxies H 0 =82±6 ± 9km/s/Mpc Summary H 0 =72±8km/s/Mpc HST Key Project (Freedman et al ApJ 553(2001)47)

17. as predicted by Inflation Cosmic age H 0 =72±8km/s/Mpc, centered around Observation: from globular cluster from cosmological nuclear chronology Concordance Model

18. Concordance Model was confirmed with high accuracy. (with the help of the HST value of Hubble parameter.)

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

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

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

24. 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. Observable quantity on Last scattering surface Integrated Sachs- Wolfe effect ： Temperature fluctuations ： Doppler effect ： Gravitational Redshift Sachs-Wolfe effect small scale Large scale They can be calculated from the Boltzman/Euler/Poisson eqs., if the initial condition of  k,t i  and cosmological parameters are given.

25. We need to calculate and at the Last scattering surface when photons and baryons are decoupled. 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. Inflation Initial condition of is also given by generated during inflation (if adiabatic fluc.)

26. LSS Θ ～ π/l d r Observer ～２ π/ k 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。 l ～ kd にピーク Fourier modes are related with angular multipoles as depicted in the figure.

27. 大スケールで ほぼ一定 小スケールで振動 流体力学的揺らぎ Sound horizon at LSS corresponds to about 1 degree, which explains the location of the peak hydorodynamical Gravitational

28. The shape of the angular power spectrum depends on （ spectral index etc ） 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 Old standard CDM model. 1 0.5 0.3 0.05 0.03 0.01 0.3 0.5 0.7 0.3 0

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