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

TL;DR

This paper derives comprehensive full-sky formulae for weak lensing power spectra using the total angular momentum method, applicable to scalar, vector, and tensor perturbations, and demonstrates their use in analyzing B-mode cosmic shear and curl-mode lensing.

Contribution

It introduces a systematic derivation of full-sky weak lensing power spectra using the TAM method, including gauge-invariant expressions and explicit formulas for various perturbations.

Findings

Derived full-sky formulae for weak lensing spectra from scalar, vector, tensor perturbations.

Presented explicit calculations of B-mode cosmic shear and curl-mode power spectra.

Simplified the computation of lensing modes using the TAM representation.

Abstract

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. This greatly simplifies the calculation, and we present a complete set of the full-sky formulae for angular power spectra in both the E-/B-mode cosmic shear and gradient-/curl-mode lensing potential of deflection angle. Based on the formulae, we give illustrative examples of non-vanishing B-mode cosmic shear and curl-mode of deflection angle in the presence of the vector and tensor perturbations, and explicitly compute the power spectra.