Testing isotropy of cosmic microwave background radiation

Abstract

We introduce new symmetry-based methods to test for isotropy in cosmic microwave background (CMB) radiation. Each angular multipole is factored into unique products of power eigenvectors, related multipoles and singular values that provide two new rotationally invariant measures mode by mode. The power entropy and directional entropy are new tests of randomness that are independent of the usual CMB power. Simulated Galactic plane contamination is readily identified. The ILC-WMAP data maps show seven axes well aligned with one another and the direction Virgo. Parameter free statistics find 12 independent cases of extraordinary axial alignment, low power entropy, or both having 5 per cent probability or lower in an isotropic distribution. Isotropy of the ILC maps is ruled out to confidence levels of better than 99.9 per cent, whether or not coincidences with other puzzles coming from the Virgo axis are included. Our work shows that anisotropy is not confined to the low l region, but extends over a much larger l range.

Alignments of parity even/odd-only multipoles in CMB

“…It's significance is assessed using Alignment entropy. The reader may refer to Ralston & Jain (2004); Samal et al (2008) for more details about the Power tensor method, as well as it's relation to axes inferred from other statistics viz. the angular momentum dispersion maximization (de Oliveira-Costa et al 2004) and Maxwell's multipole vectors (Schwarz et al 2004).…”

“…The Power tensor is a robust diagnostic to test isotropy of CMB data (Ralston & Jain 2004;Samal et al 2008Samal et al , 2009. The CMB temperature is conventionally expanded in terms of spherical harmonics Y lm (n):…”

Emergent un-Quantum Mechanics

“…[22] data from the cosmic microwave background (CMB) was analyzed to test the "cosmological principle" requiring isotropy. The alignment of spherical harmonic multipoles and the entropy of their power distribution contradicts isotropy at a high degree of statistical significance.…”

The Axis of Evil - A Polarization Perspective

“…However, in recent years, there have been claims of anomalies detected in the CMB temperature map with considerable significance, which seem to break statistical isotropy of the temperature fluctuations and thus to question the cosmological principle. Among these anomalies, there is a strong alignment between the preferred axes of the quadrupole and the octopole, which is commonly referred to as the axis of evil [3,1,11,16,15]. The claims of the existence of a preferred direction in the CMB temperature map have led to a discussion about whether this is simply due to a chance fluctuation in the CMB temperature map, if it can be blamed on local structures or on systematics in the measurement, or whether it is actually due to a preferred direction intrinsic to the geometry of the primordial Universe [4,12,17,8,13,18,10].…”