We present a new method to constrain local primordial non-Gaussianity using the large-scale modulation of the local lensing power spectrum. Our work extends our recently proposed $\pi$-field method for primordial non-Gaussianity estimation to spherical coordinates and applies it to galaxy lensing. Our approach is computationally efficient and only requires binned multipole power spectra $C_{\ell }(z_1,z_2)$ on large scales, as well as their covariance. Our method is simpler to implement than a full bispectrum estimator, but still contains the full squeezed-limit information. We validate our model using a suite of N-body simulations and demonstrate its accuracy in recovering the $f_{\mathrm{NL}}$ values. We then perform a Fisher forecast for an Legacy Survey of Space and Time-like weak lensing survey, finding ${\sigma }_{f_{\mathrm{NL}}}\simeq 44$. Our approach readily combines with other $f_{\mathrm{NL}}$-sensitive fields such as kinetic Sunyaev-Zel’dovich velocity reconstruction and clustering-based $\pi$ fields, for a future combined $f_{\mathrm{NL}}$ estimator using various large-scale galaxy and CMB observables.

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• Cosmological parameters
• Cosmology
• Inflation