# Light-Cone Observables and Gauge-Invariance in the Geodesic Light-Cone Formalism

## TL;DR

This paper proves the gauge-invariance of light-cone observable expressions in the geodesic light-cone formalism, enhancing the theoretical robustness and applicability of this coordinate system in cosmology.

## Contribution

It explicitly demonstrates the gauge-invariance of GLC expressions for key observables, filling a crucial gap in the formalism.

## Key findings

- Proved gauge-invariance of redshift, luminosity distance, and volume expressions in GLC coordinates.
- Provides a comprehensive theoretical foundation for light propagation analysis in GLC formalism.

## Abstract

The remarkable properties of the geodesic light-cone (GLC) coordinates allow analytic expressions for the light-cone observables, providing a new non-perturbative way for calculating the effects of inhomogeneities in our Universe. However, the gauge-invariance of these expressions in the GLC formalism has not been shown explicitly. Here we provide this missing part of the GLC formalism by proving the gauge-invariance of the GLC expressions for the light-cone observables, such as the observed redshift, the luminosity distance, and the physical area and volume of the observed sources. Our study provides a new insight on the properties of the GLC coordinates and it complements the previous work by the GLC collaboration, leading to a comprehensive description of light propagation in the GLC representation.