The Parity Shield

The kinematic Sunyaev-Zel'dovich (kSZ) effect imprints the peculiar velocities of galaxy clusters onto the cosmic microwave background. Reconstructing these velocities from CMB data is contaminated by foregrounds — thermal SZ, dust, and other astrophysical signals that are much brighter than the kSZ signal. Standard estimators mix signal and foreground, requiring careful foreground modeling and subtraction.

A parity-odd estimator constructed from antisymmetric tomographic correlations cancels foreground contamination entirely while preserving the full cosmological signal. The cancellation is exact, not approximate — foregrounds are eliminated by construction rather than by fitting and subtracting.

The mechanism: astrophysical foregrounds are parity-even — they correlate symmetrically between different redshift bins. The kSZ velocity signal has a parity-odd component — it correlates antisymmetrically because velocities at different distances point in systematically different directions (they trace the growth of structure, which has a specific temporal ordering). The antisymmetric estimator projects onto the parity-odd subspace, where the signal lives and the foregrounds do not.

The result is an 11-sigma detection with zero foreground bias. The estimator achieves this not by being more sensitive to the signal but by being exactly insensitive to the contamination. The full signal-to-noise of the kSZ effect is preserved because the parity-odd component carries essentially all the velocity information.

The structural observation: a symmetry distinction between signal and noise enables perfect separation. The foregrounds are not modeled, fitted, or subtracted — they are orthogonal to the measurement by construction. The antisymmetric estimator sees only what is antisymmetric, and the foregrounds are not.