Several recent papers have made claims about the detection of an asymmetric distribution of large scale power in the cosmic microwave background 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 which maximises the asymmetry between the power spectra from the corresponding hemispheres .
Such a 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 our investigation on the three specific parameters to which the analysis is most sensitive – the spectral index n , the amplitude of fluctuations A and the optical depth \tau – and find interesting variations in their estimates as determined from different hemispheres .
When using a gaussian prior on the spectral index n centred at n = 1 with a flat prior on the optical depth \tau , the preferred value for the optical depth ( derived in the reference frame of maximum asymmetry ) in the north is \tau = 0 with upper limit \tau < 0.08 , whereas in the south we find \tau = 0.24 ^ { +0.06 } _ { -0.07 } ( 68 \% confidence level ) .
The latter result is inconsistent with \tau = 0 at the 2 \sigma 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 \tau , we find values of the spectral index which are inconsistent between the opposite hemispheres .
The exact values depend on the prior on \tau .
Our conclusions remain unaltered even when , on the basis of putative residual foreground contamination , the multipole range \ell = 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 2 \sigma , if they are confirmed with the higher sensitivity WMAP 2-year data then it may be necessary to question the assumption of cosmological isotropy and the conceptual framework within which studies of the CMB anisotropy are made .