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Symmetry and anti-symmetry of the CMB anisotropy pattern

Given an arbitrary function, we may construct symmetric and antisymmetric functions under a certain operation. Since statistical isotropy and homogeneity of our Universe has been a fundamental assumption of modern cosmology, we do not expect any particular symmetry or antisymmetry in our Universe. Besides fundamental properties of our Universe, we may also figure our contamination and improve the quality of the CMB data products, by matching the unusual symmetries and antisymmetries of the CMB data with known contaminantions. Noting this, we have investigated the symmetry and antisymmetry of CMB anisotropy pattern, which provides the deepest survey. If we let the operation to be a coordinate inversion, the symmetric and antisymmetric functions have even and odd-parity respectively. The investigation on the parity of the recent CMB data shows a large-scale odd-parity preference, which is very unlikely in the statistical isotropic and homogeneous Universe. We have investigated the association of the WMAP systematics with the anomaly, but not found a definite non-cosmological cause. Additionally, we have investigated the phase of even and odd multipole data respectively, and found the behavior distinct from each other. Noting the odd-parity preference anomaly, we have fitted a cosmological model respectively to even and odd multipole data, and found significant parametric tension. Besides anomalies explicitly associated with parity, there are anomalous lack of large-scale correlation in CMB data. Noting the equivalence between the power spectrum and the correlation, we have investigated the association between the lack of large-angle correlation and the odd-parity preference of the angular power spectrum. From our analysis, we find that the odd-parity preference at low multipoles is, in fact, phenomenologically identical with the lack of large-angle correlation.