Null Cross-Correlation as a Constraint Operator: Bounding Axion–Photon Coupling from Anisotropic Cosmic Birefringence Measurements

This work formalizes the role of null-consistent cross-correlation measurements as parameter-space constraint operators in axion-photon coupling models. Using the reported cross-correlation between anisotropic cosmic birefringence and large-scale structure tracers derived from Planck NPIPE polarization products and the Quaia quasar catalog (arXiv:2509.22273) as a worked example, we distinguish detection-class claims from constraint-class claims and derive the general conditions under which null-compatible measurements yield upper limits on coupling parameters.

The reported cross-correlation amplitude is statistically consistent with zero. While no detection of anisotropic birefringence–LSS correlation is established, the measurement can be mapped into exclusion regions for axion-photon coupling within explicitly specified birefringence-generation frameworks. We provide a formal separation between observable-level null results and model-dependent parameter inference, and clarify the scope and limitations of such constraints.

We emphasize that null measurements do not constitute model-independent evidence for or against axion-like particles. Rather, when coupled to explicit theoretical mappings, they function as structured parameter-space pruning mechanisms. The constraint strength remains conditional on reconstruction systematics, tracer bias, and assumptions within the adopted cosmological framework.

This methodological analysis generalizes beyond the specific case considered and applies to any cross-correlation observable for which the theoretical prediction is a monotonic function of a coupling parameter with vanishing limit at zero coupling.

KEYWORDS

cosmic birefringence

CMB polarization

large-scale structure

cross-correlation

axion-like particles

axion-photon coupling

parameter-space constraints

null result methodology

cosmological inference

early dark energy

ultralight dark matter

model-dependent bounds

astroparticle physics

observational cosmology