The luminosity distance-redshift relation up to second order in the
  Poisson gauge with anisotropic stress
  We present the generalization of previously published results, about the
perturbed redshift and the luminosity-redshift relation up to second order in
perturbation theory, for the case of the Poisson gauge and in the presence of
anisotropic stress. The results are therefore valid for general dark energy
models and (most) modified gravity models. We use an innovative approach based
on the recently proposed "geodesic light-cone" gauge. We then compare our
finding with other results, which recently appeared in the literature, for the
particular case of vanishing anisotropic stress. Arriving at a common accepted
expression for the non-linear and relativistic corrections to the redshift and
distance-redshift relation is of fundamental importance in view of future
cosmological surveys. Thanks to these surveys the Universe will be further
probed with high precision and at very different scales, where non-linear and
relativistic effects can play a key role.
