# Observation angles, Fermi coordinates, and the Geodesic-Light-Cone gauge

## TL;DR

This paper demonstrates that in a generic cosmological background, the angles measured by a static observer in Fermi Normal Coordinates match those in the GLC gauge, with a specific gauge-fixing condition ensuring their full identification.

## Contribution

It establishes a precise relationship between Fermi Normal Coordinates and the GLC gauge for observational angles in cosmology, and proposes a gauge-fixing condition for exact angle identification.

## Key findings

- Angles in Fermi Normal Coordinates match GLC gauge angles locally.
- The residual gauge freedom in GLC allows for this angle correspondence.
- A specific GLC gauge-fixing condition ensures full observational angle identification.

## Abstract

We show that the angular directions locally measured by a static geodesic observer in a generic cosmological background and expressed in the system of Fermi Normal Coordinates always coincide with those expressed in the Geodesic-Light-Cone (GLC) gauge, up to a local transformation which exploits the residual gauge freedom of the GLC coordinates. This is not the case for other gauges - like, for instance, the synchronous and longitudinal gauge - commonly used in the context of observational cosmology. We also make an explicit proposal for the GLC gauge-fixing condition that ensures a full identification of its angles with the observational ones.