Geometric optics in relativistic cosmology: New formulation and a new observable

Abstract

We discuss a new formalism for light propagation which can be used within the regime of validity of geometric optics, but with no limitation on the scales of interest: from inside the Galaxy to the ultralarge scales of cosmology. One of our main results is that within this framework it is possible to calculate all relevant observables (image magnification, parallax, position drift or proper motion) by simply differentiating the photon trajectory with respect to the initial data. We then focus on a new observable, which we name the distance slip: it is defined as the relative difference between the angular diameter distance and the parallax distance. Its peculiarity lies in the fact that its value is independent of the momentary motions of both the source and the observer and that for short distances it shows a tomographic property, being proportional to the amount of matter along the line of sight. After describing further its properties and methods of measurement, we specialize our study of the distance slip to cosmology. We show that it does not depend on the Hubble constant ${H}_{0}$ and that its dependence on the other cosmological parameters is different from other distance indicators. This suggests that the distance slip may contain new information.