We test the tenet of statistical isotropy of the standard cosmological model
via a homology analysis of the cosmic microwave background temperature maps.
Examining small sectors of the normalized maps, we find that the results
exhibit a dependence on whether we compute the mean and variance locally from
the masked patch, or from the full masked sky. Assigning local mean and
variance for normalization, we find the maximum discrepancy between the data
and model in the galactic northern hemisphere at more than 3.5 s.d. for the
PR4 dataset at degree-scale. For the PR3 dataset, the C-R and SMICA maps
exhibit higher significance than the PR4 dataset at ∼4 and 4.1 s.d.
respectively, however the NILC and SEVEM maps exhibit lower significance at
∼3.4 s.d. The southern hemisphere exhibits high degree of consistency
between the data and the model for both the PR4 and PR3 datasets. Assigning the
mean and variance of the full masked sky decreases the significance for the
northern hemisphere, the tails in particular. However the tails in the southern
hemisphere are strongly discrepant at more than 4 standard deviations at
approximately 5 degrees. The p-values obtained from the χ2-statistic
exhibit commensurate significance in both the experiments. Examining the
quadrants of the sphere, we find the first quadrant to be the major source of
the discrepancy. Prima-facie, the results indicate a breakdown of statistical
isotropy in the CMB maps, however more work is needed to ascertain the source
of the anomaly. Regardless, these map characteristics may have serious
consequences for downstream computations such as parameter estimation, and the
related Hubble tension.Comment: 13 pages, 10 figures, 3 table