Light propagation in the averaged universe
  Cosmic structures determine how light propagates through the Universe and
consequently must be taken into account in the interpretation of observations.
In the standard cosmological model at the largest scales, such structures are
either ignored or treated as small perturbations to an isotropic and
homogeneous Universe. This isotropic and homogeneous model is commonly assumed
to emerge from some averaging process at the largest scales. We assume that
there exists an averaging procedure that preserves the causal structure of
space-time. Based on that assumption, we study the effects of averaging the
geometry of space-time and derive an averaged version of the null geodesic
equation of motion. For the averaged geometry we then assume a flat
Friedmann-Lema\^{i}tre (FL) model and find that light propagation in this
averaged FL model is not given by null geodesics of that model, but rather by a
modified light propagation equation that contains an effective Hubble expansion
rate, which differs from the Hubble rate of the averaged space-time.
