Detection of the ISW effect and corresponding dark energy constraints made with directional spherical wavelets

Using a directional spherical wavelet analysis we detect the integrated Sachs-Wolfe (ISW) effect, indicated by a positive correlation between the Wilkinson Microwave Anisotropy Probe (WMAP) and NRAO VLA Sky Survey (NVSS) data, at the 3.9$\sigma$ level. Detections are made at this level using both a directional extension of the spherical Mexican hat wavelet and the spherical butterfly wavelet. The wavelet analysis inherently enables us to localise on the sky those regions that contribute most strongly to the correlation. On removing these localised regions the correlation that we detect is reduced in significance, as expected, but it is not eliminated suggesting that these regions are not the sole source of correlation between the data. This finding is consistent with predictions made using the ISW effect. We use our detection of the ISW effect to constrain dark energy parameters by deriving a theoretical prediction for the directional wavelet covariance statistic for a given cosmological model. Comparing these predictions with the data we place constraints on the equation-of-state parameter w (assumed to be constant during the epoch of interest) and the vacuum energy density $\Omega_\Lambda$. All parameter estimates that we obtain are consistent with the standand cosmological concordance model values. Although wavelets perform very well when attempting to detect the ISW effect since one may probe only the regions where the signal is present, once all information is incorporated when computing parameter estimates the performance of the wavelet analysis is comparable to other methods, as expected for a linear approach.