The second-order luminosity-redshift relation in a generic inhomogeneous
  cosmology
  After recalling a general non-perturbative expression for the
luminosity-redshift relation holding in a recently proposed "geodesic
light-cone" gauge, we show how it can be transformed to phenomenologically more
convenient gauges in which cosmological perturbation theory is better
understood. We present, in particular, the complete result on the
luminosity-redshift relation in the Poisson gauge up to second order for a
fairly generic perturbed cosmology, assuming that appreciable vector and tensor
perturbations are only generated at second order. This relation provides a
basic ingredient for the computation of the effects of stochastic
inhomogeneities on precision dark-energy cosmology whose results we have
anticipated in a recent letter. More generally, it can be used in connection
with any physical information carried by light-like signals traveling along our
past light-cone.
