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

We present a $2.5\sigma$ 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 ($\Delta z\sim 0.03$) and an approximately volume limited redshift distribution from $z\sim 0.2$ to $z\sim 0.6$ 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 $2.5\sigma$ signal in the Ka, Q, V, and W WMAP bands, after combining the information from multipoles $2\le l<400$. 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 ${\Omega }_M=0.3$, ${\Omega }_{\Lambda }=0.7$, and ${\sigma }_8=0.9$, is $b_g=4.05\pm 1.54$ for V band, with similar results for the other bands. This should be compared to $b_g=1.82\pm 0.02$ from the autocorrelation analysis. These data provide only a weak confirmation ($2.5\sigma$) of dark energy but provide a significant upper limit: ${\Omega }_{\Lambda }={0.80}_{-0.06}^{+0.03}(1\sigma {)}_{-0.19}^{+0.05}(2\sigma )$, assuming a cosmology with ${\Omega }_M+{\Omega }_{\Lambda }=1$, ${\Omega }_b=0.05$, ${\sigma }_8=0.9$, 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 $({\Omega }_M,{\sigma }_8,w)$. 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.