  We study the Voronoi volume function (VVF) -- the distribution of cell
volumes (or inverse local number density) in the Voronoi tessellation of any
set of cosmological tracers (galaxies/haloes). We show that the shape of the
VVF of biased tracers responds sensitively to physical properties such as halo
mass, large-scale environment, substructure and redshift-space effects, making
this a hitherto unexplored probe of both primordial cosmology and galaxy
evolution. Using convenient summary statistics -- the width, median and a low
percentile of the VVF as functions of average tracer number density -- we
explore these effects for tracer populations in a suite of N-body simulations
of a range of dark matter models. Our summary statistics sensitively probe
primordial features such as small-scale oscillations in the initial matter
power spectrum (as arise in models involving collisional effects in the dark
sector), while being largely insensitive to a truncation of initial power (as
in warm dark matter models). For vanilla cold dark matter (CDM) cosmologies,
the summary statistics display strong evolution and redshift-space effects, and
are also sensitive to cosmological parameter values for realistic tracer
samples. Comparing the VVF of galaxies in the GAMA survey with that of
abundance matched CDM (sub)haloes tentatively reveals environmental effects in
GAMA beyond halo mass (modulo unmodelled satellite properties). Our exploratory
analysis thus paves the way for using the VVF as a new probe of galaxy
evolution physics as well as the nature of dark matter and dark energy.
