First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Dark Energy Induced Correlation with Radio Sources

TL;DR

The paper tests the dark-energy-driven late ISW effect by cross-correlating the first-year WMAP CMB map with the NVSS radio-source catalog. Using a flat $\Lambda$CDM framework and the ISW formalism, they compute the cross-correlation spectrum $C^{NT}_l$ and the angular cross-correlation function, accounting for a modeled redshift distribution and bias of NVSS sources. They find a preference for $\Omega_\Lambda>0$ with a peak near $\Omega_\Lambda \approx 0.68$ and $\Delta\chi^2 = 4.7$ relative to the null case, disfavoring a matter-dominated universe at about the 3$\sigma$ level; the result provides an independent check of cosmic acceleration. The authors discuss potential systematics, including dust extinction and possible microwave emission from NVSS sources, and conclude the observed signal is robust and broadly consistent with the standard $\Lambda$CDM interpretation of dark energy.

Abstract

The first-year WMAP data, in combination with any one of a number of other cosmic probes, show that we live in a flat Λ-dominated CDM universe with Ω_m ~ 0.27 and Ω_Λ~ 0.73. In this model the late-time action of the dark energy, through the integrated Sachs-Wolfe effect, should produce CMB anisotropies correlated with matter density fluctuations at z<2 (Crittenden & Turok 1996). The measurement of such a signal is an important independent check of the model. We cross-correlate the NRAO VLA Sky Survey radio source catalog (Condon et al. 1998) with the WMAP data in search of this signal, and see indications of the expected correlation. Assuming a flat Λ-CDM cosmology, we find Ω_Λ>0 (95% CL, statistical errors only) with the peak of the likelihood at Ω_Λ=0.68, consistent with the preferred WMAP value. A closed model with Ω_m=1.28, h=0.33, and no dark energy component (Ω_Λ=0), marginally consistent with the WMAP CMB TT angular power spectrum, would produce an anti-correlation between the matter distribution and the CMB. Our analysis of the cross-correlation of the WMAP data with the NVSS catalog rejects this cosmology at the 3σlevel.

Figures (4)

• Figure 1: The gravitational potential $\Phi$ as a function of redshift $z$ for a variety of cosmological models. The models are normalized to unity at $z=0$.
• Figure 2: The adopted $dN/dz$ model (RLF1) for the distribution of NVSS sources from dunlop/peacock:1990, normalized to integrate to unity (left panel). The small blip at $z\approx0.05$ is spurious, due to breakdown in the DP90 fitting function. Also plotted is the "luminosity/density evolution" (LDE) model also from DP90, which is a poor fit to the observed auto-correlation function (right panel).
• Figure 3: The WMAP--NVSS cross-correlation function (CCF). The CCF is insensitive to the details of the declination correction. Two simple methods are compared; both broke the sources into $\sin(\delta)$ strips of width $0.1$. The first (diamonds) subtracted the mean from each strip. The second (triangles) scaled each strip by the ratio of the global mean to the strip mean. The cross points are uncorrected, showing the correction is only important for $\theta\ga 25$. We used the WMAP internal linear combination (ILC) CMB map; substituting the map of tegmark/deoliveira-costa/hamilton:2003 instead produces the same results (square points). The solid and dashed lines are derived from the diagonal elements of the correlation matrix due to accidental alignments; they would be the $1\sigma$ and $2\sigma$ contours in the absence of off-diagonal correlations. The points, however, are highly correlated as shown in Table \ref{['tbl:sim_corr_matrix']}.
• Figure 4: Effect of varying $\Omega_\Lambda$ on the cross-correlation function. In all panels we assume a flat universe with fixed $\omega_b$, and trade off between $\Omega_\Lambda$ and $h$ by keeping the combination $\Omega_m h^{3.4}$ constant; when $\Omega_\Lambda=0$, $h=0.48$. Panel (a) shows the inferred radio bias as a function of $\Omega_\Lambda$. Panel (b) shows the bias-corrected NVSS auto-correlation function (ACF) compared with the measured ACF. Panel (c) shows the predicted cross-correlation function (CCF) for a range of values of $\Omega_\Lambda$, compared with the measured CCF (diamonds). The amplitude of the predicted CCF is proportional to $\Omega_\Lambda$, which is stepped in increments of 0.1 from 0.0 to 0.9. Panel (d) shows the $\chi^2$ of the model CCF as a function of $\Omega_\Lambda$. The $\chi^2$ was computed using the first 10 points of the CCF ($0\arcdeg<\theta<20\arcdeg$) and Table \ref{['tbl:sim_corr_matrix']}. The minimum $\chi^2_{\rm min}$ is $12.5$ at $\Omega_\Lambda=0.68$; at $\Omega_\Lambda=0$, $\chi^2_0=17.2$. The dashed line is the likelihood $\propto \exp(-\chi^2/2)$. The $1\sigma$ limits are $0.42<\Omega_\Lambda<0.86$.