Geometric optics in relativistic cosmology: new formulation and a new
  observable
  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 ultra-large 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.
