1. Dark energy I : Observational constraints Shinji Tsujikawa (Tokyo University of Science)

2. Dark energy From the observations of SN Ia, CMB, and BAO etc, about 70 % of the energy density of the Universe is dark energy responsible for cosmic acceleration.

3. Observational constraints on dark energy The properties of dark energy can be constrained by a number of observations: 1.Supernovae type Ia (SN Ia) 2. Cosmic Microwave Background (CMB) 3.Baryon Acoustic Oscillations (BAO) 4. Large-scale structure (LSS) 5.Weak lensing The cosmic expansion history is constrained. The evolution of matter perturbations is constrained. This is especially important for modified gravity models.

4. Supernovae Ia observations The luminosity distance L s : Absolute lumonisity F : Observed flux is related with the Hubble parameter H, as for the flat Universe (K=0) The absolute magnitude M of SN Ia is related with the observed apparent magnitude m, via

5. Luminosity distance in the flat Universe

6. Luminosity distance with/without dark energy Flat Universe without dark energy Open Universe without dark energy Flat Universe with dark energy

7. Perlmutter et al, Riess et al (1998) (Perlmutter et al, 1998) Perlmutter et al showed that the cosmological constant ( ) is present at the 99 % confidence level, with the matter density parameter The rest is dark energy. High-z data A. Riess B. Schmidt (Head of Perlmutter et al group)

8. Observational constraints on the dark energy equation of state for constant w (Kowalski et al, 2008) SN Ia data only DE

9. Time-varying dark energy equation of state

10. where Parametrization of the dark energy equation of state

11. Best-fit case Observational constraints using the parametrization Komatsu et al (2010) Zhao et al (2007) (SNIa, WMAP, SDSS)

12. Observational constraints from CMB The observations of CMB temperature anisotropies can also place constraints on dark energy. 2012 PLANCK data will be released.

13. CMB temperature anisotropies Dark energy affects the CMB anisotropies in two ways. 1. Shift of the peak position 2. Integrated Sachs Wolfe (ISW) effect ISW effect Larger Smaller scales (Important for large scales) Shift for

14. Angular diameter distance The angular diameter distance is (flat Universe) (duality relation)

15. Causal mechanism for the generation of perturbations Second Hubble radius crossing After the perturbations leave the Hubble radius during inflation, the curvature perturbations remain constant by the second Hubble radius crossing. Scale-invariant CMB spectra on large scales After the perturbations enter the Hubble radius, they start to oscillate as a sound wave. Physical wavelength Hubble radius

16. CMB acoustic peaks where HuSugiyama

17. (CMB shift parameter) where and

18. The WMAP 7-yr bound:

19. (Komatsu et al, WMAP 7-yr) Observational constraints on the dark energy equation of state Flat Universe

20. Joint data analysis of SN Ia + CMB (for constant w ) The constraints from SN Ia and CMB are almost orthogonal. DE (Kowalski et al, 2008) DE (0)

21. ISW effect on CMB anisotropies

22. Evolution of matter density perturbations ( ) The growing mode solution is Responsible for large-scale structure Perturbations do not grow.

23. Poisson equation The Poisson equation is given by (i) During the matter era (ii) During the dark energy era (no ISW effect)

24. Usually the constraint coming from the ISW effect is not so tight compared to that from the CMB shift parameter. (apart from some modified gravity models) ISW effect

25. CMB lensing The Atacama Cosmology telescope found the observational evidence of w = -1 dark energy from the CMB data alone by using the new CMB lensing data (2011). The lensing deflection spectrum is

26. Baryon Acoustic Oscillations (BAO) Baryons are tightly coupled to photons before the decoupling. The oscillations of sound waves should be imprinted in the baryon perturbations as well as the CMB anisotropies. In 2005 Eisenstein et al found a peak of acoustic oscillations in the large scale correlation function at

27. BAO distance measure The sound horizon at which baryons were released from the Compton drag of photons determines the location of BAO: We introduce (orthogonal to the line of sight) (the oscillations along the line of sight) The spherically averaged spectrum is

28. We introduce the relative BAO distance where The observational constraint by Eisenstein et al is The case (i) is favored.

29. Observational constraints on the dark energy equation of state from the joint data analysis of SN Ia + CMB + BAO Kowalski et al