Light propagation in linearly perturbed $\Lambda$LTB models

TL;DR

This paper develops a formalism to analyze light propagation in linearly perturbed spherically symmetric dust models with a cosmological constant, enabling better testing of the Copernican Principle using lensing observables.

Contribution

It introduces a gauge-invariant approach to relate perturbation variables to lensing quantities and provides a method to compute shear and convergence in these models.

Findings

Derived differential equations for lensing observables in perturbed models.

Mapped perturbation variables to weak lensing quantities like shear and convergence.

Presented spherical harmonic coefficients of lensing signals including E- and B-modes.

Abstract

We apply a generic formalism of light propagation to linearly perturbed spherically symmetric dust models including a cosmological constant. For a comoving observer on the central worldline, we derive the equation of geodesic deviation and perform a suitable spherical harmonic decomposition. This allows to map the abstract gauge-invariant perturbation variables to well-known quantities from weak gravitational lensing like convergence or cosmic shear. The resulting set of differential equations can effectively be solved by a Green's function approach leading to line-of-sight integrals sourced by the perturbation variables on the backward lightcone. The resulting spherical harmonic coefficients of the lensing observables are presented and the shear field is decomposed into its E- and B-modes. Results of this work are an essential tool to add information from linear structure formation to the analysis of spherically symmetric dust models with the purpose of testing the Copernican Principle with multiple cosmological probes.