Testing the cosmological principle of isotropy: local power spectrum   estimates of the WMAP data
  We apply the Gabor transform methodology proposed in (Hansen et al. 2002, 2003) to the WMAP data in order to test the statistical properties of the CMB fluctuation field and specifically to evaluate the fundamental assumption of cosmological isotropy. We estimate the angular power spectrum locally in discs of various sizes positioned in different directions. We determine whether the spatial position of a few outliers in the angular power spectrum could suggest the presence of residual foregrounds or systematic effects. For multipoles close to the first peak, the most deviant local estimates from the best fit WMAP model are associated with a few particular areas close to the Galactic plane. Such deviations also include the ``dent'' in the spectrum just shortward of the first peak which was remarked upon by the WMAP team. Estimating the angular power spectrum excluding these areas gives a slightly higher first Doppler peak amplitude. Finally, we probe the isotropy of the largest angular scales by estimating the power spectrum on hemispheres and reconfirm strong indications of a north-south asymmetry previously reported by other authors. We find tentative evidence for residual foregrounds in the range l=2-4, which could be associated with the low measured quadrupole amplitudes and other anomalies on these angular scales. However, over the range l=5-40 the observed asymmetry is much harder to explain in terms of residual foregrounds and known systematic effects. Such asymmetric distributions of power on the sky provide a serious test for the cosmological principle of isotropy. 
F. K. Hansen, A. J. Banday, K. M. Gorski