Testing Statistical Isotropy in the FRB Sky Distribution: A Selection-Function-Aware Framework
We perform a test of statistical isotropy in the Universe using the sky distribution of fast radio bursts (FRBs), based on a compilation of $4066$ events detected by multiple surveys. Our method is based on the two-point angular correlation function $w(θ)$ as in the Landy--Szalay estimator, together with a tomographic absolute-anisotropy statistic, and estimates their observational uncertainties from complementary jackknife and bootstrap resampling. Both estimators are confronted with hierarchical ensembles of isotropic mock catalogs that propagate the uncertainties of empirically reconstructed survey selection functions, as well as the Poisson fluctuations of the isotropic realizations. The significances are obtained from a covariance-aware, SVD-regularized $χ^2$ statistic calibrated empirically against the mock ensemble, and we evaluate four nested scenarios that progressively incorporate a Galactic-plane mask and the survey selection functions. As for our results, we find that the raw FRB sky is strongly inconsistent with isotropy; Galactic masking alone reduces the tension by only a factor of $\sim 3$, whereas the selection functions reduce it by nearly four orders of magnitude, showing that the apparent anisotropy is driven by the highly non-uniform sky coverage of the contributing surveys, overwhelmingly dominated by CHIME. Only when both effects are combined we obtain that the observed distribution is fully consistent with statistical isotropy. This result is independently corroborated by the absolute-anisotropy estimator, and is stable under variations of the analysis parameters. Therefore, we find that the FRB sky distribution is consistent with statistical isotropy, helping confirm one of the main predictions of the standard model scenario.