Recovering Density Fields inside Quasar Proximity Zones at $z\sim 6$
  The matter density field at $z\sim 6$ is very challenging to probe. One of
the traditional probes of the low density IGM that works successfully at lower
redshifts is the Lyman-alpha forest in quasar spectra. However, at the end of
reionization, the residual neutral hydrogen usually creates saturated
absorption, thus much of the information about the gas density is lost.
Luckily, in a quasar proximity zone, the ionizing radiation is exceptionally
intense, thus creating a large region with non-zero transmitted flux. In this
study we use the synthetic spectra from simulations to investigate how to
recover the density fluctuations inside the quasar proximity zones. We show
that, under ideal conditions, the density can be recovered accurately with a
small scatter. We also discuss how systematics such as the quasar continuum
fitting and reionization models affect the results. This study shows that by
analyzing the absorption features inside quasar proximity zones we can
potentially constrain quasar properties and the environments they reside in.
