Cross-Correlation of 2MASS with WMAP3: Implications for ISW Anaïs Rassat (University College London) Kate Land (Imperial College London) Ofer Lahav (University College London)

Integrated Sachs-Wolfe Effect

2MASS Galaxy Survey Publicly available eXtended Source Catalogue (XSC) J, H, K bands (Near Infrared) ~1,650,000 Galaxies with magnitudes corrected for Galactic extinction. Analysis includes 69% sky & 1,250,000 Galaxies Compare with Cabré et al (SDSS DR4): ~16% (z ~ 1) Scranton et al (SDSS – LRGs) : ~ 8% (z ~ 0.45) Fosalba and Gaztañaga 2003 (APM): ~10% (z ~ 0.15)

2MASS ⊗ WMAP3 Auto-Correlation Cross-Correlation AoE statistic

Auto-Correlation Function: ACF EXACT IN LINEAR THEORY

Constant linear bias b from C gg (ℓ) 12 < K 20 < 14

Best fit

2MASS ⊗ WMAP3 Auto-Correlation√ Cross-Correlation AoE statistic

3 rd Year WMAP Foreground reduced maps of Q,V and W bands Q band (41 GHz) V band (61 GHz) W band (94 GHz) Images from WMAP Science Team

Method: Follow Afshordi et al (WMAP1 ⊗ 2MASS) Perform Cross-Correlation in Harmonic Space: Cut Kp2 mask on WMAP3, Cut out 31% of 2MASS sky

ALL of 2MASS with ILC map CORRELATION?

Colourful Correlation

2MASS 4 Magnitude Bins with ILC map POSITIVE CORRELATION TREND FOR LOW MULTIPOLES?

Four Magnitude Shells ⊗ Q, V, W, ILC WMAP3 maps Achromatic Trend 1σ from 500 simulations of CMB with 2MASS WMAP3 / 2MASS

Changes between WMAP1 & WMAP3 ■ WMAP3 □ WMAP1 Why is there a difference?

Theory Exact in linear theory: Small angle approximation:

Predicted Cross-Correlation: Exact & Small Angle Approximation: ℓ ~ 11

Shells with z ~ (> gal) z ~ (> gal) ∆χ 2 = χ 2 ISW - χ 2 NULL = 2 ☼

OPEN COSMOLOGIES

Or f ~ 1.7 (~1.6)

Model Dependent Statistic Assume there is Dark Energy in a Ω k =0 Universe C gT [DATA] = h* C gT [ISW_fiducial] Without prior on σ8:h ~ 1.7 or 2σ detection (Null detection corresponds to h < 0) With prior on σ8:h ~ 1.6 Etc.. Full Parameter Space needs to be investigated

ALTERNATIVE FIDUCIAL MODELS h ~ 1.7 2σ Detection

2MASS ⊗ WMAP3 Auto-Correlation √ Cross-Correlation√ AoE statistic

Axis of Evil ☼ ℓ=2 ℓ=3ℓ=4ℓ=5 WMAP3 2MASS

Summary: 2MASS ⊗ WMAP3 WMAP3 ⊗ 2MASS : within 1σ [NULL] (Model Independent) ISW (fiducial) : within 1σ [NULL] C gT DATA ~ 1.7 C gT FIDUCIAL (Model Dependent 2σ Detection) AoE(WMAP) ≠ AoE(2MASS) Thanks to Filipe Abdalla, Niayesh Afshordi, Sarah Bridle, Carlo Contaldi, for comments, advice and assistance.

CCL Find 2MASS b = 1.4 Cross-correlate 2MASS with WMAP3: –Slight change from 2MASS with WMAP1 –Visible positive achromatic cross-correlation, suggestive of ISW effect, but also consistent with Null Hypothesis. –Data fits ISW effect “too well” –Marginalization over parameter space makes cross- correlation even less significant. Axis of Evil: other statistical test –No significant correlation between AOE of WMAP and