Symmetry and anti-symmetry of the CMB anisotropy pattern

Understand

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.