Measures of non-Gaussianity in axion-string-induced CMB birefringence

The presence of axion strings in the Universe after recombination can leave an imprint on the polarization pattern of the cosmic microwave background radiation through the phenomenon of axion-string-induced birefringence via the hyperlight axion-like particle's coupling to electromagnetism. Across the sky, the polarization rotation angle is expected to display a patchwork of uniform regions with sharp boundaries that arise as the `shadow' of axion string loops. The statistics of such a birefringence sky map are therefore necessarily non-Gaussian. In this article we quantify the non-Gaussianity in axion-string-induced birefringence using two techniques, kurtosis and bispectrum, which correspond to $4$- and $3$-point correlation functions. If anisotropic birefringence were detected in the future, a measurement of its non-Gaussian properties would facilitate a discrimination across different new physics sources generally, and in the context of axion strings specifically, it would help to break degeneracies between the axion-photon coupling and properties of the string network.