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

Understand

We systematically derive full-sky formulae for the weak lensing power spectra generated by scalar, vector and tensor perturbations from the total angular momentum (TAM) method.

• Based on both the geodesic and geodesic deviation equations, we first give the gauge-invariant expressions for the deflection angle and Jacobi map as observables of the CMB lensing and cosmic shear experiments.
• We then apply the TAM method, originally developed in the theoretical studies of CMB, to a systematic derivation of the angular power spectra.
• The TAM representation, which characterizes the total angular dependence of the spatial modes projected along a line-of-sight, can carry all the information of the lensing modes generated by scalar, vector, and tensor metric perturbations.