Ricci focusing, shearing, and the expansion rate in an almost
  homogeneous Universe
  The Universe is inhomogeneous, and yet it seems to be incredibly
well-characterised by a homogeneous relativistic model. One of the current
challenges is to accurately characterise the properties of such a model. In
this paper we explore how inhomogeneities may affect the overall optical
properties of the Universe by quantifying how they can bias the
redshift-distance relation in a number of toy models that mimic the real
Universe. The models that we explore are statistically homogeneous on large
scales. We find that the effect of inhomogeneities is of order of a few
percent, which can be quite important in precise estimation of cosmological
parameters. We discuss what lessons can be learned to help us tackle a more
realistic inhomogeneous universe.
