Testing the cosmological principle of isotropy: local power spectrum estimates of the WMAP data

Abstract

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.

Figures (25)

• Figure 1: The position and numbering of the $9.5^\circ$ discs on which the local power spectra have been calculated.
• Figure 2: The disc-disc correlation matrix for the multipole bins 0, 3 and 6 centred at $\ell=33$, $\ell=189$ and $\ell=339$ respectively.
• Figure 3: Slice of the disc correlation matrix for some selected discs at the lowest multipole bin $\ell=33$ and a bin centred close to the first power spectrum peak $\ell=189$. We have chosen the discs 0,6 and 60 in order to study the correlations for discs which have many (disc 0) and few (disc 6 and 60) overlapping neighbours. The other discs have been chosen as particular bin values of these discs have been found in the WMAP data. We have chosen particular discs close to the ecliptic poles as some particular features are found in this area (see the text and figure \ref{['fig:plotdisc4_b034']})
• Figure 4: Slice of the bin to bin correlation matrix for disc 0 taken at bins 1,4,5 and 9.
• Figure 5: The best fit WMAP running index power spectrum (solid line). The histogram shows the spectrum binned using the same bins as for the disc estimates. The crosses show the binned full sky WMAP spectrum obtained by the WMAP team and the shaded areas show the spread of the WMAP spectrum over 130 discs of radius $9.5^\circ$, found from the Gabor analysis. The two shaded areas indicate where 67 and 95 percent of the 130 WMAP disc estimates are contained. Note that the shaded areas are NOT error bars for the WMAP estimates, but the spread found by estimating the spectrum in different positions.