A new approach to the propagation of light-like signals in perturbed
  cosmological backgrounds
  We present a new method to compute the deflection of light rays in a
perturbed FLRW geometry. We exploit the properties of the Geodesic Light Cone
(GLC) gauge where null rays propagate at constant angular coordinates
irrespectively of the given (inhomogeneous and/or anisotropic) geometry. The
gravitational deflection of null geodesics can then be obtained, in any other
gauge, simply by expressing the angular coordinates of the given gauge in terms
of the GLC angular coordinates. We apply this method to the standard Poisson
gauge, including scalar perturbations, and give the full result for the
deflection effect in terms of the direction of observation and observed
redshift up to second order, and up to third order for the leading lensing
terms. We also compare our results with those presently available in the
literature and, in particular, we provide a new non trivial check of a previous
result on the luminosity-redshft relation up to second order in cosmological
perturbation theory.
