Conceptual problems in detecting the evolution of dark energy when using
  distance measurements
  Dark energy is now one of the most important and topical problems in
cosmology. The first step to reveal its nature is to detect the evolution of
dark energy or to prove beyond doubt that the cosmological constant is indeed
constant. However, in the standard approach to cosmology, the Universe is
described by the homogeneous and isotropic Friedmann models. Here we show that
in the perturbed universe (even if perturbations vanish if averaged over
sufficiently large scales) the distance-redshift relation is not the same as in
the unperturbed universe. This has a serious consequence when studying the
nature of dark energy and, as shown here, can impair the analysis and studies
of dark energy. The analysis is based on two methods: the linear lensing
approximation and the non-linear Szekeres Swiss-Cheese model. The inhomogeneity
scale is ~50 Mpc, and both models have the same density fluctuations along the
line of sight. The comparison between linear and non-linear methods shows that
non-linear corrections are not negligible. When inhomogeneities are present the
distance changes by several percent. To show how this change influences the
measurements of dark energy, ten future observations with 2% uncertainties are
generated. It is shown the using the standard methods (i.e. under the
assumption of homogeneity) the systematics due to inhomogeneities can distort
our analysis, and may lead to a conclusion that dark energy evolves when in
fact it is constant (or vice versa). Therefore, if future observations are
analysed only within the homogeneous framework then the impact of
inhomogeneities (such as voids and superclusters) can be mistaken for evolving
dark energy. Since the robust distinction between the evolution and
non-evolution of dark energy is the first step to understanding the nature of
dark energy a proper handling of inhomogeneities is essential.
