Cross-correlation of the CMB and radio galaxies in real, harmonic and wavelet spaces: detection of the integrated Sachs-Wolfe effect and dark energy constraints

We report the first detection of the ISW effect in wavelet space, at scales in the sky around 7 degrees with a significance of around 3.3 sigma, by cross-correlating the WMAP first-year data and the NRAO VLA Sky Survey (NVSS). In addition, we present a detailed comparison among the capabilities of three different techniques for two different objectives: to detect the ISW and to put constraints in the nature of the dark energy. The three studied techniques are: the cross-angular power spectrum (CAPS, harmonic space), the correlation function (CCF, real space) and the covariance of the Spherical Mexican Hat Wavelet (SMHW) coefficients (CSMHW, wavelet space). We prove that the CSMHW is expected to provide a higher detection of the ISW effect for a certain scale. This prediction has been corroborated by the analysis of the data. The SMHW analysis shows that the cross-correlation signal is caused neither by systematic effects nor foreground contamination. However, by taking into account the information encoded in all the multipoles/scales/angles, the CAPS provides slightly better constraints than the SMHW in the cosmological parameters that define the nature of the dark energy. The limits provided by the CCF are wider than for the other two methods. Two different cases have been studied: 1) a flat Lambda-CDM universe and 2) a flat universe with an equation of state parameter different from -1. In the first case, the CAPS provides (for a bias value of b = 1.6) 0.59 < Lambda density < 0.84 (at 1 sigma CL). Moreover, the CAPS rejects the range Lambda density < 0.1 at 3.5 sigma, which is the highest detection of the dark energy reported up to date. In the second case, the CAPS gives 0.50 < dark energy density < 0.82 and -1.16 < w < 0.43 (at 1 sigma CL).