Detection of the integrated Sachs–Wolfe 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 first-year Wilkinson Microwave Anisotropy Probe (WMAP) and NRAO VLA Sky Survey (NVSS) data. Detections are made using both a directional extension of the spherical Mexican hat wavelet and the spherical butterfly wavelet. We examine the possibility of foreground contamination and systematics in the WMAP data and conclude that these factors are not responsible for the signal that we detect. The wavelet analysis inherently enables us to localize on the sky those regions that contribute most strongly to the correlation. On removing these localized 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, where one would expect weak correlations over the entire sky. In a flat universe the detection of the ISW effect provides direct and independent evidence for dark energy. We use our detection 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 and the vacuum energy density ΩΛ. We also consider the case of a pure cosmological constant, that is, w=−1. For this case we rule out a zero cosmological constant at greater than the 99.9 per cent significance level. All parameter estimates that we obtain are consistent with the standard 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.