Integrated Sachs-Wolfe effect from the cross correlation of WMAP3 year and the NRAO VLA sky survey data: New results and constraints on dark energy

TL;DR

This study detects a late-time ISW signal by cross-correlating the WMAP3 CMB map with the NVSS radio-galaxy catalog using a novel spherical needlet framework. By modeling dark energy with the three-parameter fluid description ($\Omega_{DE}$, $w$, $c_s^2$) and keeping other cosmological parameters fixed to WMAP3 best fits, the authors derive robust evidence for non-zero dark energy density and place constraints that depend on the dark-energy sound speed. LCDM with $w=-1$ remains a good fit, though the $w$ bounds broaden as $c_s^2$ changes, and phantom models are disfavored for $c_s^2=1$; overall the results highlight ISW as a powerful probe of dark energy's clustering properties. The use of needlets improves localization and reduces sky-cut effects, suggesting that future, deeper surveys could tighten these constraints and potentially reveal ISW signals at higher redshifts.

Abstract

We cross-correlate the new 3 year Wilkinson Microwave Anistropy Probe (WMAP) cosmic microwave background (CMB) data with the NRAO VLA Sky Survey (NVSS) radio galaxy data, and find further evidence of late integrated Sachs-Wolfe (ISW) effect taking place at late times in cosmic history. Our detection makes use of a novel statistical method \cite{Baldi et al. 2006a, Baldi et al. 2006b} based on a new construction of spherical wavelets, called needlets. The null hypothesis (no ISW) is excluded at more than 99.7% confidence. When we compare the measured cross-correlation with the theoretical predictions of standard, flat cosmological models with a generalized dark energy component parameterized by its density, $\omde$, equation of state $w$ and speed of sound $\cs2$, we find $0.3\leq\omde\leq0.8$ at 95% c.l., independently of $\cs2$ and $w$. If dark energy is assumed to be a cosmological constant ($w=-1$), the bound on density shrinks to $0.41\leq\omde\leq 0.79$. Models without dark energy are excluded at more than $4σ$. The bounds on $w$ depend rather strongly on the assumed value of $\cs2$. We find that models with more negative equation of state (such as phantom models) are a worse fit to the data in the case $\cs2=1$ than in the case $\cs2=0$.

Figures (7)

• Figure 1: The function dN/dz used for the sources in the NVSS in our analysis. The dotted curve is the theoretical model from Dunlop Peacock 1990, which has a spurious feature due to the breakdown of the fit at low z. The continuous line is the fit adopted in our analysis.
• Figure 2: Plots of the needlet basis $\psi_{jk}$ for an arbitrary value of $k$ and three representative values of $j$: continuous line $j=7$, dotted line $j=8$, dashed line $j=9$. Note that the angle in the $x$ axis is measured on the geodesic, not on the tangent plane.
• Figure 3: Effect of the sky cut on the estimated needlet coefficients. Pixels $k$ corresponding to values of the estimator $D_{jk}$ above a given threshold are shown in black, and are clearly concentrated only very close to the masked regions. For this figure, $j=11$. From top to bottom, the threshold for $D_{jk}$ takes the values 0.1, 0.25, 0.5.
• Figure 4: The wavelet cross-correlation power spectrum $\beta_j$ of the WMAP and NVSS maps. The points represent the signal extracted from the real data, with error bars given by Eq. \ref{['errors']}. The continuos line is the average of the cross-correlation power spectra obtained when 1000 simulated CMB fiducial data sets are correlated with the real NVSS map: this measures the level of correlation expected from casual alignment. The shaded area is the $1\sigma$ dispersion of the simulated spectra.
• Figure 5: Constraints at 68%, 95% and 99% confidence level in the $\Omega_{\rm DE}$---$w$ plane. The upper panel was obtained under the hypothesis that the dark energy speed of sound is $c_s^2=0$; the lower panel was obtained for $c_s^2=1$.