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 including the form of the simplistic density field considered and the survey geometry.