Correlating the CMB with Luminous Red Galaxies : The Integrated Sachs-Wolfe Effect

TL;DR

The paper targets the ISW effect by cross-correlating WMAP CMB temperature maps with SDSS LRG overdensities across a large sky area, using an inverse-variance quadratic estimator and ISW-shaped templates to optimally extract the signal. By combining the cross-correlation with an auto-correlation-based bias constraint, the authors derive constraints on the matter density and dark-energy properties in a flat ΛCDM framework, reporting a 2.5σ detection and a best-fit Ω_M ≈ 0.20 with 1σ range ~0.17–0.26. The results provide a weak but meaningful confirmation of dark energy and place a robust lower bound on Ω_M, while highlighting that joint constraints on Ω_M and the equation of state w require additional data; the paper also offers a practical method to incorporate ISW information into cosmological parameter estimation. Overall, the study demonstrates the ISW signal as a complementary probe of dark energy and outlines paths for stronger future constraints with expanded sky coverage and improved redshift characterization.

Abstract

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 WMAP satellite with a 4000 deg^2 luminous red galaxy (LRG) overdensity map measured by the Sloan Digital Sky Survey. Accurate photometric redshifts allow us to perform a reliable auto-correlation analysis of the LRGs, eliminating the uncertainty in the galaxy bias, and combined with cross correlation signal, constrains cosmological parameters -- in particular, the matter density. We find a 2.5 sigma 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 σ_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 auto-correlation analysis. These data provide only a weak confirmation (2.5 sigma) of dark energy, but provide a significant upper limit: Ω_Λ=0.80_{-0.06}^{+0.03} (1 sigma)_{-0.19}^{+0.05} (2 sigma), assuming a cosmology with Ω_M+Ω_Λ=1, Ω_b = 0.05, and σ_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 (Ω_M, σ_8,w). (abridged)

Figures (12)

• Figure 1: Predictions for the ISW signal given the redshift distribution of LRGs described in Sec. \ref{['sec:lrg']}, $b_{g}=1$, $\sigma_{8}=0.9$, and a flat universe. The different curves show the effect of changing the matter density. In particular, observe that the effect becomes stronger as the matter density decreases.
• Figure 2: The LRG redshift distribution. The histogram shows the photometric redshift distribution, the curve is the true redshift distribution estimated by regularized deconvolution of the photo-$z$ errors. The dotted lines show the photometric redshift cuts imposed at $z=0.2$ and $0.6$.
• Figure 3: The LRG angular distribution in Galactic coordinates. The gaps in the distribution are due to the stellar mask, nonphotometric data, and Galactic extinction.
• Figure 4: The cross correlation between WMAP and the SDSS LRG density, as measured in flat bandpowers for the four WMAP bands considered in the paper. Also plotted is predicted ISW signal for a $\Omega_{M}=0.3, \Omega_{\Lambda}=0.7$ universe, scaled by the measured galaxy bias in Table \ref{['tab:bias']}. Note that these power spectra have been beam-deconvolved.
• Figure 5: Conditional contour plots of the galaxy density as a function of the stellar density and galactic extinction, $E(B-V)$. The contours are the 5%, 50% and 95% contours, while the horizontal line is the mean galaxy density. Also shown are the correlation coefficients, $r$ for both datasets. There is no evidence for significant stellar contamination or incorrect extinction corrections in these data.