Perturbative treatment of the luminosity distance
  We derive a generalized luminosity distance versus redshift relation for a
linearly perturbed FLRW (Friedmann-Lemaitre-Robertson-Walker) metric with two
scalar mode excitations. We use two equivalent approaches, based on the Jacobi
map and the van Vleck determinant respectively. We apply the resultant formula
to two simple models - an exact FLRW universe and an approximate FLRW universe
perturbed by a single scalar mode sinusoidally varying with time. For both
models we derive a cosmographic expansion for d_L in terms of z. We comment on
the interpretation of our results and their possible application to more
realistic cosmological models.
