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

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

Constraint of Dark energy

In a flat universe: 0, 1 0, 0

0 0, 0

linm

lin

If P

If P

( / ) /d D a dt

Imprint on the CMB Power spectrum

Cooray 2002 Hu 2001The 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…

Cross-correlation of LSS & CMB

( / ) /d D a dz

N(z)

ISW fluctuations are correlated with galaxy distributionGalaxies are bias tracer to large scale structure

b(t): Galaxy bias parameterN(t): Galaxy selection function

Sky covrerage: 5.5×5.5 deg2, Survey Depth: mean z~0.15

APM-WMAP cross-correlation

Fosalba & Gaztanag 2004;

SZ

ISW

Galaxy survey with CMB map

Cabre et al. 2006

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 energyLarge sky coverage: improving S/N

ISW + Rees-Sciama + SZ + Lensing + Doppler redshift + …

You may expect more than ISW…

WMAP sees hereWMAP sees here

Sunyaev-Zel’dovich effect

Doppler effectLensing magnification

LOS

tSZ

Moving halo effect

ISW+Dop+LenISW+Dop

ISW

Seljak 1995; Afshordi et al. 2004; Fosalba & Gaztanag 2004; LoVerde et al. 2007

Rees-Sciama effect SZ effect

Power spectra of thepotential 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 ISW

Cai et al. in prep.

ISW + RSISW + RS

Cai et al. in prep.

2-D Power spectra of the potential derivative measured from the L-BASICC simulation.

L-BASICC simulation is the LambdaCDMcosmology with

Deviation of the total power spectrum from linear theory occurs at larger scales as redshift increase.

ISW ISW

ISW + RSISW + RS

8

0.75, 25,

0.024, 0.9

m

b

Cai et al. in prep.

ISW + RSISW + RS

ISWISW

ISW cross-correlation

Cai et al. in prep.

ISW + RSISW + RS

ISWISW

ISW cross-correlation

Summary Cross-correlation of LSS & CMB provides co

nstraint 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 imp

ortant on the scale of a few degrees Accurate modeling of the RS effect would b

e useful