  One of the most exciting advances of the current generation of telescopes has
been the detection of galaxies during the epoch of reionization, using deep
fields that have pushed these instruments to their limits. It is essential to
optimize our analyses of these fields in order to extract as much information
as possible from them. In particular, standard methods of measuring the galaxy
luminosity function discard information on large-scale dark matter density
fluctuations, even though this large-scale structure drives galaxy formation
and reionization during the Cosmic Dawn. Measuring these densities would
provide a bedrock observable, connecting galaxy surveys to theoretical models
of the reionization process and structure formation. Here, we use existing
Hubble deep field data to simultaneously fit the universal luminosity function
and measure large-scale densities for each Hubble deep field at $z =$ 6--8 by
directly incorporating priors on the large-scale density field and galaxy bias.
Our fit of the universal luminosity function is consistent with previous
methods but differs in the details. For the first time, we measure the
underlying densities of the survey fields, including the most over/under-dense
Hubble fields. We show that the distribution of densities is consistent with
current predictions for cosmic variance. This analysis on just 17 fields is a
small sample of what will be possible with the James Webb Space Telescope,
which will measure hundreds of fields at comparable (or better) depths and at
higher redshifts.
