Jacobi map and physical observables: an exact solution in the GLC gauge
We present an exact non-perturbative expression for the Jacobi map within the framework of the recently proposed Geodesic Light-Cone Gauge. This is a system of coordinates fixed on the past light-cone of the observer: this feature simplify a lot the expressions involved. Moreover, some important physical observables can be expressed thanks to this solution: the main one is the angular distance (or, equivalently, the luminosity distance). This new result nicely takes in account all of the aberration effects at the observer, in particular the one related to the observer's peculiar velocity. We also prove this by transforming our formula in two well-known gauge: the Synchronous and the Longitudianal one.