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We systematically derive full-sky formulae for the weak lensing power spectragenerated by scalar, vector and tensor perturbations from the total angularmomentum (TAM) method. Based on both the geodesic and geodesic deviationequations, we first give the gauge-invariant expressions for the deflectionangle and Jacobi map as observables of the CMB lensing and cosmic shearexperiments. We then apply the TAM method, originally developed in thetheoretical studies of CMB, to a systematic derivation of the angular powerspectra. The TAM representation, which characterizes the total angulardependence of the spatial modes projected along a line-of-sight, can carry allthe information of the lensing modes generated by scalar, vector, and tensormetric perturbations. This greatly simplifies the calculation, and we present acomplete set of the full-sky formulae for angular power spectra in both theE-/B-mode cosmic shear and gradient-/curl-mode lensing potential of deflectionangle. Based on the formulae, we give illustrative examples of non-vanishingB-mode cosmic shear and curl-mode of deflection angle in the presence of thevector and tensor perturbations, and explicitly compute the power spectra.

Full-sky formulae for weak lensing power spectra from total angular momentum method