A new approach to the propagation of light-like signals in perturbed cosmological backgrounds

TL;DR

This paper introduces a novel method using the Geodesic Light Cone gauge to compute light deflection in perturbed cosmological backgrounds, simplifying calculations and enabling higher-order accuracy.

Contribution

The authors develop a new approach leveraging the GLC gauge to efficiently compute light deflection in perturbed FLRW geometries, including higher-order effects.

Findings

Derived full second-order deflection expressions in Poisson gauge.

Provided third-order leading lensing term results.

Validated the method with existing luminosity-redshift relation results.

Abstract

We present a new method to compute the deflection of light rays in a perturbed FLRW geometry. We exploit the properties of the Geodesic Light Cone (GLC) gauge where null rays propagate at constant angular coordinates irrespectively of the given (inhomogeneous and/or anisotropic) geometry. The gravitational deflection of null geodesics can then be obtained, in any other gauge, simply by expressing the angular coordinates of the given gauge in terms of the GLC angular coordinates. We apply this method to the standard Poisson gauge, including scalar perturbations, and give the full result for the deflection effect in terms of the direction of observation and observed redshift up to second order, and up to third order for the leading lensing terms. We also compare our results with those presently available in the literature and, in particular, we provide a new non trivial check of a previous result on the luminosity-redshft relation up to second order in cosmological perturbation theory.