Redshift and distances in a {\Lambda}CDM cosmology with non-linear
  inhomogeneities
  Motivated by the dawn of precision cosmology and the wealth of forthcoming
high precision and volume galaxy surveys, in this paper we study the effects of
inhomogeneities on light propagation in a flat \Lambda CDM background. To this
end we use exact solutions of Einstein's equations (Meures & Bruni 2011) where,
starting from small fluctuations, inhomogeneities arise from a standard growing
mode and become non-linear. While the matter distribution in these models is
necessarily idealised, there is still enough freedom to assume an arbitrary
initial density profile along the line of sight. We can therefore model
over-densities and voids of various sizes and distributions, e.g. single
harmonic sinusoidal modes, coupled modes, and more general distributions in a
\Lambda CDM background. Our models allow for an exact treatment of the light
propagation problem, so that the results are unaffected by approximations and
unambiguous. Along lines of sight with density inhomogeneities which average
out on scales less than the Hubble radius, we find the distance redshift
relation to diverge negligibly from the Friedmann-Lemaitre-Robertson-Walker
(FLRW) result. On the contrary, if we observe along lines of sight which do not
have the same average density as the background, we find large deviations from
the FLRW distance redshift relation. Hence, a possibly large systematic might
be introduced into the analysis of cosmological observations, e.g. supernovae,
if we observe along lines of sight which are typically more or less dense than
the average density of the Universe. In turn, this could lead to wrong
parameter estimation: even if the Cosmological Principle is valid, the
identification of the true FLRW background in an inhomogeneous universe maybe
more difficult than usually assumed.
