Correlation of CMB with large-scale structure: I. ISW Tomography and Cosmological Implications

TL;DR

This work performs an ISW tomography by cross-correlating WMAP CMB maps with diverse LSS tracers (2MASS, SDSS LRGs and QSOs, NVSS) across z ~ 0–2.5, building a full covariance and a forward-modeling framework to derive cosmological constraints. It develops a detailed redshift-distrubition and bias modeling for each tracer, including magnification effects, and delivers a robust likelihood for comparing cosmological models, not merely detecting the ISW signal. The analysis yields a combined ISW detection of 3.7σ, constraining curvature to Ω_K = -0.004^{+0.014}_{-0.020} and the dark energy equation of state to w = -1.01^{+0.30}_{-0.40} when combined with CMB lensing, showing ISW's power to test geometry and late-time evolution even amid systematics. The results illustrate the potential and challenges of ISW tomography for distinguishing cosmological models and for probing non-standard gravity, and set the stage for future improvements with deeper surveys and improved CMB data.

Abstract

We cross-correlate large scale structure (LSS) observations from a number of surveys with CMB anisotropies from WMAP to investigate the Integrated Sachs-Wolfe (ISW) effect as a function of redshift, covering z~0.1-2.5. Our main goal is to go beyond reporting detections towards developing a reliable likelihood analysis that allows one to determine cosmological constraints from ISW observations. With this in mind we spend a considerable amount of effort in determining the redshift-dependent bias and redshift distribution b(z)*dN/dz of these samples by matching with spectroscopic observations where available, and analyzing auto-power spectra and cross-power spectra between the samples. The data sets we use are 2-Micron All Sky Survey (2MASS) samples, Sloan Digital Sky Survey (SDSS) photometric Luminous Red Galaxies, SDSS photometric quasars and NRAO VLA Sky Survey (NVSS) radio sources. We make a joint analysis of all samples constructing a full covariance matrix, which we subsequently use for cosmological parameter fitting. We report a 3.7 sigma detection of ISW combining all the datasets. We combine the ISW likelihood function with weak lensing of CMB and CMB power spectrum to constrain the equation of state of dark energy and the curvature of the Universe. While ISW does not significantly improve the constraints in the simplest 6-parameter flat Lambda CDM model, it improves constraints on 7-parameter models with curvature by a factor of 3.2 (relative to WMAP alone) to Omega_K=-0.004^{+0.014}_{-0.020}, and with dark energy equation of state by 15% to w=-1.01^{+0.30}_{-0.40}. (Abridged.)

Figures (18)

• Figure 1: The overdensity maps of various tracer samples in Galactic coordinates. The scale runs from $g=-1$ (black, no galaxies) to $g=-0.25$ (blue), $g=0$ (green), $g=+0.25$ (red), and $g=+1$ (white, $\ge 2\times$ mean density).
• Figure 2: LRG and QSO overdensity vs various quantities such as reddening, PSF FWHM ($r$ band), observing time (MJD), red star density, and star density. In each panel the circles show the low-redshift sample and the squares show the high-redshift sample. The Modified Julian Date (MJD) of the DR3 ending date is 52821. Note that there are very few accepted pixels at the extremes of reddening, PSF FWHM, and stellar density, resulting in the large fluctuations seen in the figure.
• Figure 3: Galaxy density correlations with WMAP temperatures (4 bands: Ka (crosses), Q (triangles), V (squares), W (empty triangles), error bars are from the correlations with V-band. This contains 2MASS galaxy density correlations with WMAP, starting from (from left to right, top to bottom) the brightest sample, to the bottom the dimmest sample. We shift the points on x-axis for clarity. The dotted line shows the predicted signal for the sample with WMAP 3-year parameters and $b dN/dz$ estimated in Sec. \ref{['sec:dndz']}.
• Figure 4: Same as Fig. \ref{['fig:cross_2mass']} except for the SDSS density maps from (from left to right, top to bottom): low-z LRG, high-z LRG, low-z QSO, high-z QSO.
• Figure 5: Same as Fig. \ref{['fig:cross_2mass']} except for the NVSS cross-correlation.