High-redshift voids in the excursion set formalism

Voids are a dominant feature of the low-redshift galaxy distribution. Several recent surveys have found evidence for the existence of large-scale structure at high redshifts as well. We present analytic estimates of galaxy void sizes at redshifts z ~ 5 - 10 using the excursion set formalism. We find that recent narrow-band surveys at z ~ 5 - 6.5 should find voids with characteristic scales of roughly 20 comoving Mpc and maximum diameters approaching 40 Mpc. This is consistent with existing surveys, but a precise comparison is difficult because of the relatively small volumes probed so far. At z ~ 7 - 10, we expect characteristic void scales of ~ 14 - 20 comoving Mpc assuming that all galaxies within dark matter haloes more massive than 10^10 M_sun are observable. We find that these characteristic scales are similar to the sizes of empty regions resulting from purely random fluctuations in the galaxy counts. As a result, true large-scale structure will be difficult to observe at z ~ 7 - 10, unless galaxies in haloes with masses less than ~ 10^9 M_sun are visible. Galaxy surveys must be deep and only the largest voids will provide meaningful information. Our model provides a convenient picture for estimating the "worst-case" effects of cosmic variance on high-redshift galaxy surveys with limited volumes.