Shear B Modes

Weak gravitational lensing measures the shapes of background galaxies distorted by foreground mass distributions, and the estimated shapes contain both an E-mode (curl-free) component sourced by gravitational lensing and a B-mode (curl) component that should be zero for pure gravitational lensing in the standard framework. Residual B-modes in weak lensing catalogs arise from observational systematics — PSF modeling errors, intrinsic alignment contamination, and noise biases — rather than from any physical signal. Multiple weak lensing surveys have found residual B-mode power at levels that are marginally inconsistent with their estimated systematic error budgets, suggesting either that systematic control is more challenging than anticipated or that there is a genuine physical source of B-mode power not captured in the standard framework. The pattern of B-mode residuals across surveys shows a non-trivial angular scale dependence and cross-correlations with large-scale structure tracers that are difficult to explain as purely instrumental artifacts.

Successive Collision Theory provides a physical source of genuine weak lensing B-modes through the angular momentum inheritance mechanism and the non-zero vorticity field of the matter velocity distribution. In standard lensing theory, the lensing convergence is a pure E-mode because it is sourced by the scalar gravitational potential, and B-modes can only arise from tensor perturbations or vector modes that standard perturbation theory predicts to be negligibly small at late times. However, in SCT, the non-zero vorticity field inherited from the collision angular momentum constitutes a genuine vector perturbation in the velocity field that persists to the present day — it is not a decaying relic but a conserved angular momentum component maintained by Noether's theorem. This vorticity contributes to the shear field through the coupling between velocity and density perturbations in the nonlinear regime, generating a small but non-zero B-mode contribution to the weak lensing signal that is sourced by physical angular momentum rather than by systematic errors.

The amplitude of the SCT weak lensing B-mode signal is set by the ratio of rotational to irrotational velocity power at the scales probed by each survey, which in turn is determined by the angular momentum content of the debris field at those scales. SCT predicts the B-mode power should peak at angular scales corresponding to the characteristic angular momentum injection scale of the collision — a scale comparable to the cosmic web filament width — and fall off at both larger and smaller scales. The B-mode angular power spectrum should be correlated with the E-mode through the cross-correlation of the angular momentum field with the density field, producing a non-zero EB cross-power that is a uniquely physical signal distinguishable from PSF-generated systematics that would not produce this specific spatial correlation. Detection of the SCT-predicted EB correlation in future surveys from Euclid and the Rubin Observatory would constitute direct observational evidence for the angular momentum inheritance mechanism at cosmological scales — an elegant final confirmation that the collision geometry's angular momentum imprint permeates the universe from the smallest bound structures to the largest lensing surveys.