Symmetry of the CMB sky as a new test of its statistical isotropy. Non Cosmological Octupole?

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In this article we propose a novel test for statistical anisotropy of the CMB.

• The test is based on the fact, that the Galactic foregrounds have a remarcably strong symmetry with respect to their antipodal points and with respect to the Galactic plane, while the cosmological signal should not be symmetric or asymmetric under these transitions.
• We have applied the test for the octupole component of the WMAP ILC 7 map, by looking at a_3,1 and a_3,3, and their ratio to a_3,2 both for real and imaginary values.
• We find abnormal symmetry of the octupole component at the level of 0.58%, compared to Monte Carlo simulations.