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

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.