Cosmological homogeneity scale estimates are dressed
  We investigate number count statistics as measures for transition to
homogeneity of the matter distribution in the Universe and analyse how such
statistics might be `dressed' by the assumed survey selection function. Since
the estimated survey selection function -- which ideally accounts for selection
bias in the observed distribution -- is partially degenerate with the estimated
underlying distribution of galaxies, the ability to identify the correct survey
selection function is of importance for obtaining reliable estimates for
clustering statistics. Selection functions of existing galaxy catalogues are
modelled from data to resemble the redshift distribution and mean density of
the observed galaxies. Proposed estimates of the selection function for
upcoming surveys in addition use the angular distribution of galaxies to
generate the angular selection function instead of using angular completeness
estimates. We argue that such modelling of the selection function could
potentially underestimate the deviance from homogeneity at scales probed by
existing catalogues. We investigate the impact of conventionally applied
methods for estimation of the survey selection function on number count in
sphere statistics in a toy model setting. The example density distribution is
asymptotically homogeneous, while non-linear density fluctuations are present
regionally. We find that density oscillations with period comparable to
characteristic scales of the survey are suppressed when conventional estimates
of the survey selection function are invoked, resulting in number count
statistics that are biased towards homogeneity. For our concrete toy model with
maximum density contrasts of 1 and period of the density oscillation comparable
in size to the survey radius, we find that the homogeneity scale is
underestimated by ~40%, however this quantitative result is dependent on the
model setup.
