Bipolar Power Spectrum

The bipolar power spectrum (BiPS) is a statistical tool that measures correlations between pairs of CMB multipoles that are otherwise assumed independent in a rotationally invariant universe. Nonzero BiPS signal indicates a breakdown of statistical isotropy — that the universe has an intrinsic directionality at some angular scale. ΛCDM inflation predicts zero BiPS at all scales; observed hints of nonzero signal are anomalous within that framework. In SCT, the collision event endows the thermalized plasma with angular momentum whose direction defines a preferred axis. This axis breaks statistical isotropy: pairs of multipoles whose combined angular momentum projects onto the collision axis are correlated, while pairs projecting perpendicular to that axis are not. The BiPS therefore measures a real physical quantity in SCT — the projection of the collision angular momentum onto the multipole decomposition of the sky.

The expected BiPS signal in SCT is concentrated at low multipoles (ℓ ∼ 2–20) because the collision geometry imprints coherence on the largest angular scales, while smaller-scale fluctuations are generated by the standard Jeans instability and acoustic physics after thermalization and inherit no special directional correlation. This predicted multipole dependence of the BiPS signal is observationally distinguishable from alternative explanations such as foreground contamination, which would produce a signal at higher multipoles correlated with Galactic emission. The BiPS thus represents a targeted observable that can in principle discriminate between SCT's collision-geometry origin and instrumental or foreground explanations of the observed isotropy violation.