Volume Statistics as a Probe of Large-Scale Structure
  We investigate the application of volume statistics to probe the distribution
of underdense regions in the large-scale structure of the Universe. This
statistic measures the distortion of Eulerian volume elements relative to
Lagrangian ones and can be built from tracer particles using tessellation
methods. We apply Voronoi and Delaunay tessellation to study the clustering
properties of density and volume statistics. Their level of shot-noise
contamination is similar, as both methods take into account all available
tracer particles in the field estimator. The tessellation causes a smoothing
effect in the power spectrum, which can be approximated by a constant window
function on large scales. The clustering bias of the volume statistic with
respect to the dark matter density field is determined and found to be
negative. We further identify the Baryon Acoustic Oscillation (BAO) feature in
the volume statistic. Apart from being smoothed out on small scales, the BAO is
present in the volume power spectrum as well, without any systematic bias.
These observations suggest that the exploitation of volume statistics as a
complementary probe of cosmology is very promising.
