Cosmological parameters and the WMAP data revisited

Several recent papers have made claims about the detection of an asymmetric distribution of large-scale power in the cosmic microwave background (CMB) anisotropy as measured by the WMAP satellite. In this paper, we investigate how the estimates of particular cosmological parameters vary when inferred from power spectra computed separately on the Northern and Southern hemispheres in three frames of reference: the galactic, the ecliptic and the specific frame of reference that maximizes the asymmetry between the power spectra from the corresponding hemispheres. The study is intended to quantify the consistency of the observed spectral variations in the context of the inflationary scenario inspired models with which the data are commonly compared. We focus on the three specific parameters to which the analysis is most sensitive (spectral index n, amplitude of fluctuations A and optical depth) and find interesting variations in their estimates as determined from different hemispheres. Only multipoles in the ranges l = 2- 60, 200- 240 and 520- 560 (the latter two around the first two peaks) are included in the analysis. Polarization information could not be used since the appropriate sky maps are not publicly available. Furthermore, we fix Omega(Lambda) = 0.74, Omega(cdm) h(2) = 0.11 and Omega(total) = 1 atthese best-fitting values obtained by the WMAP team, and use a Gaussian prior centred at Omega(b)h(2) = 0.022 with sigma = 0.001 for the baryon fraction. No significant changes to the conclusions were found when these parameters were varied. When using a Gaussian prior on the spectral index n centred at n = 1 with a flat prior on the optical depth, the preferred value for the optical depth (derived in the reference frame of maximum asymmetry) in the Northern hemisphere is tau = 0 with upper limit tau < 0.08, whereas in the Southern hemisphere we find = 0.24(-0.07)(+0.06) (68 per cent confidence level). The latter result is inconsistent with = 0 at the 2sigma level. The estimated optical depth of tau = 0.17 on the (nearly) full sky found by the WMAP collaboration, and confirmed independently here, could thus in large part originate in structure associated with the Southern hemisphere. Furthermore, putting a prior on,we find values of the spectral index that are inconsistent between the two hemispheres. The exact values depend on the prior on. Our conclusions remain unaltered even when, on the basis of putative residual foreground contamination, the multipole range l = 2- 7 is excluded from the analysis. While our results should not be considered more than suggestive, the significance of the parameter differences in the two hemispheres being typically of order 2sigma ,if they are confirmed with the higher-sensitivity WMAP 2-yr data, then it may be necessary to question the assumption of cosmological isotropy and the conceptual framework within which studies of CMB anisotropy are made.