We report on the first detection of the integrated Sachs-Wolfe (ISW) effect in wavelet space, at scales in the sky around θ≈ 7° with a significance ≈3.3σ, by cross-correlating the Wilkinson Microwave Anisotropy Probe (WMAP) first-year data and the National Radio Astronomy Observatories (NRAO) Very Large Array (VLA) Sky Survey (NVSS). In addition, we present a detailed comparison of the capabilities of three different techniques for two different objectives: to detect the ISW effect and to put constraints on 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 (in terms of the signal-to-noise ratio) of the ISW effect for a certain scale. However, the detection achieved by the CAPS is the lowest, being the signal-to-noise ratio dispersed among a wide multipole range. The CCF provides an intermediate detection level. 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, although the three of them give similar confidence levels (CLs). Two different cases have been studied: (i) a flat λ cold dark matter universe; (ii) a flat universe with an equation of state parameter that, although it does not change with time, could take values different from −1. In the first case, the CAPS provides (for a bias value of b= 1.6) Ωλ= 0.73+0.11−0.14 (at 1σ CL). Moreover, the CAPS rejects the range Ωλ < 0.1 at ≈3.5σ, which is the highest detection of dark energy reported to date. In the second case, the CAPS gives ΩDE= 0.70+0.12−0.20 and w=−0.75+0.32−0.41 (at 1σ CL). This is the first estimation of the equation of state of dark energy made through the cross-correlation of the cosmic microwave background (CMB) and the nearby galaxy density distribution. It also provides an independent estimation from that made by the WMAP team using the CMB and large-scale structure.

We acknowledge the financial support provided through the European Community's Human Potential Programme under contract HPRN-CT-2000-00124, CMBNET, and partial financial support from the Spanish MEC projects ESP2002-04141-C03-01 and ESP2004-07067-C03-01. PV thanks IN2P3 (CNRS) for a postdoctoral contract. We acknowledge the use of LAMBDA, support for which is provided by the NASA Office of Space Science.

Peer reviewed