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.
