Correlating the CMB with luminous red galaxies: The integrated Sachs-Wolfe effect

We present a 2.5σ detection of the Integrated Sachs-Wolfe (ISW) effect and discuss the constraints it places on cosmological parameters. We cross correlate microwave temperature maps from the Wilkinson microwave anisotropy probe (WMAP) satellite with a 4000  deg⁡² luminous red galaxy (LRG) overdensity map measured by the Sloan Digital Sky Survey. These galaxies have accurate photometric redshifts (Δz∼0.03) and an approximately volume limited redshift distribution from z∼0.2 to z∼0.6 well suited to detecting the ISW effect. Accurate photometric redshifts allow us to perform a reliable autocorrelation analysis of the LRGs, eliminating the uncertainty in the galaxy bias, and combined with the cross correlation signal, constrains cosmological parameters—in particular, the matter density. We use a minimum-variance power spectrum estimator that optimally weights the data according to expected theoretical templates. We find a 2.5σ signal in the Ka, Q, V, and W WMAP bands, after combining the information from multipoles 2≤l<400. This is consistent with the expected amplitude of the ISW effect but requires a lower matter density than is usually assumed: the amplitude, parametrized by the galaxy bias assuming Ω_M=0.3, Ω_Λ=0.7, and σ₈=0.9, is b_g=4.05±1.54 for V band, with similar results for the other bands. This should be compared to b_g=1.82±0.02 from the autocorrelation analysis. These data provide only a weak confirmation (2.5σ) of dark energy but provide a significant upper limit: Ω_Λ=0.80_-0.06^+0.03(1σ)_-0.19^+0.05(2σ), assuming a cosmology with Ω_M+Ω_Λ=1, Ω_b=0.05, σ₈=0.9, and w=-1. The weak cross correlation signal rules out low matter density/high dark energy density universes and, in combination with other data, strongly constrains models with w<-1.3. We provide a simple prescription to incorporate these constraints into cosmological parameter estimation methods for (Ω_M,σ₈,w). We find no evidence for a systematic contamination of ISW signal, either from galactic or extragalactic sources, but we do detect some large statistical fluctuations on smaller scales that could affect analyses without the template weighting.