# Full-sky weak lensing: a nonlinear post-Friedmann treatment

## TL;DR

This paper develops a comprehensive full-sky weak lensing model within the Post-Friedmann formalism, capturing relativistic and non-linear effects across scales, and explores measurable impacts of frame-dragging on lensing observables.

## Contribution

It introduces a full-sky weak lensing framework in the Post-Friedmann formalism, including relativistic and non-linear effects, and analyzes the impact of vector perturbations on lensing measurements.

## Key findings

- Derived lensing observables up to order 1/c^4 including relativistic effects.
- Identified how frame-dragging vector potentials influence lensing signals.
- Discussed potential observational signatures of vector perturbations in future surveys.

## Abstract

We present a full-sky derivation of weak lensing observables in the Post-Friedmann (PF) formalism. Weak lensing has the characteristic of mixing small scales and large scales since it is affected by inhomogeneities integrated along the photon trajectory. With the PF formalism, we develop a modelling of lensing observables which encompasses both leading order relativistic effects and effects that are due to the fully non-linear matter distribution at small scales. We derive the reduced shear, convergence and rotation up to order $1/c^4$ in the PF approximation, accounting for scalar, vector and tensor perturbations, as well as galaxies' peculiar velocities. We discuss the various contributions that break the Kaiser-Squires relation between the shear and the convergence at different orders. We pay particular attention to the impact of the frame-dragging vector potential on lensing observables and we discuss potential ways to measure this effect in future lensing surveys.