Homology reveals significant anisotropy in the cosmic microwave background

We test the tenet of statistical isotropy of the standard cosmological model via a homology analysis of the cosmic microwave background (CMB) temperature maps in galactic coordinates. The map pixels were normalized by subtracting the mean and rescaling by standard deviation, both of which were computed from the relevant unmasked pixels. 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 non-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 northern hemisphere, at more than 3.5 standard deviations (s.d.) for the PR4 dataset at degree scale. For the PR3 dataset, the C-R and SMICA maps display a higher significance than the PR4 dataset at ∼4 and 4.1 s.d., respectively; however, the NILC and SEVEM maps present a lower significance at ∼3.4 s.d. The discrepancy is most prominent at scales of roughly a degree, which coincides with the physical scale of the horizon at the epoch of the CMB. The southern hemisphere exhibits a 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; in particular, the tails. 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 χ 2 -statistic show commensurate significance in both experiments. Examining the quadrants of the sphere, we find the northwest quadrant of the Galactic frame 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 and parameter estimation, and the related problems of Hubble and σ 8 tension.