Probing the Cosmological Principle with CMB lensing and cosmic shear

The standard cosmological model assumes the Cosmological Principle. However, recent observations hint at possible violations of isotropy on large scales, possibly through late-time anisotropic expansion. Here we investigate the potential of cross-correlations between CMB lensing convergence $\kappa$ and galaxy cosmic shear $B$-modes as a novel probe of such late-time anisotropies. Our signal-to-noise forecasts reveal that information from the $\kappa$-$B$ cross-correlation is primarily contained on large angular scales ($\mathrm{\ell }\lesssim 200$). We find that this cross-correlation for a Euclid-like galaxy survey is sensitive to anisotropy at the percent level. Making use of tomography yields a modest improvement of $\sim 20\mathrm{\%}$ in detection power. Incorporating the galaxy $E$-$B$ cross-correlations would further enhance these constraints.