  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).
