1. Yanchuan Cai ( 蔡彦川 ) Shaun Cole, Adrian Jenkins, Carlos Frenk Institute for Computational Cosmology Durham University May 31, 2008, NDHU, Taiwan ISW Cross-Correlation

2. Potential decay – ISW effect  Linear regime – Integrated Sachs-Wolfe effect (ISW) (Sachs & Wolfe 1967)  Non-linear regime - Rees-Sciama effect (RS) (Rees & Sciama 1968)  ISW & RS effect capture the dynamics of the universe  Potential change induce secondary CMB temperature fluctuation

3. Constraint of Dark energy In a flat universe:

4. Imprint on the CMB Power spectrum Cooray 2002Hu 2001 The ISW effect is difficult to be detected from the CMB power spectrum due to cosmic variance. The Rees-Sciama effect is negligible for the CMB PS, but…

5. Cross-correlation of LSS & CMB N(z)  ISW fluctuations are correlated with galaxy distribution  Galaxies are bias tracer to large scale structure b(t): Galaxy bias parameter N(t): Galaxy selection function

6. Sky covrerage: 5.5×5.5 deg 2, Survey Depth: mean z~0.15 APM-WMAP cross-correlation Fosalba & Gaztanag 2004; SZ ISW Galaxy survey with CMB map

7. Cabre et al. 2006

8. ISW Tomography – Dark Energy Evolution LSST Pan-STARRS Cai et al. in preparation; Hu & Scranton 2004; LoVerde et al. 2007  Deep galaxy survey: detection of the evolution of dark energy  Large sky coverage: improving S/N

9. ISW + Rees-Sciama + SZ + Lensing + Doppler redshift + … You may expect more than ISW…

10. WMAP sees here Sunyaev-Zel’dovich effect Doppler effect Lensing magnification LOS tSZ Moving halo effect

11. ISW+Dop+Len ISW+Dop ISW Seljak 1995; Afshordi et al. 2004; Fosalba & Gaztanag 2004; LoVerde et al. 2007 Rees-Sciama effect SZ effect

12.  Power spectra of the potential derivative measured from the L-BASICC simulation.  The second order contribution can be well modeled by a broken power law.  Deviation of the total power spectrum from linear theory occurs at larger scales as redshift Increase.ISW Cai et al. in prep. ISW + RS

13. Cai et al. in prep.  2-D Power spectra of the potential derivative measured from the L-BASICC simulation.  L-BASICC simulation is the LambdaCDM cosmology with  Deviation of the total power spectrum from linear theory occurs at larger scales as redshift increase.ISW ISW + RS

14. Cai et al. in prep. ISW + RS ISW ISW cross- correlation

15. Cai et al. in prep. ISW + RS ISW ISW cross- correlation

16. Summary  Cross-correlation of LSS & CMB provides constraint to dark energy  ISW tomography is promising, but hard  Separating ISW, SZ, lensing magnification, Doppler effect, Rees-Sciama effect…  RS effect dominates at high-z, could be important on the scale of a few degrees  Accurate modeling of the RS effect would be useful