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We study the Voronoi volume function (VVF) -- the distribution of cellvolumes (or inverse local number density) in the Voronoi tessellation of anyset of cosmological tracers (galaxies/haloes). We show that the shape of theVVF of biased tracers responds sensitively to physical properties such as halomass, large-scale environment, substructure and redshift-space effects, makingthis a hitherto unexplored probe of both primordial cosmology and galaxyevolution. Using convenient summary statistics -- the width, median and a lowpercentile of the VVF as functions of average tracer number density -- weexplore these effects for tracer populations in a suite of N-body simulationsof a range of dark matter models. Our summary statistics sensitively probeprimordial features such as small-scale oscillations in the initial matterpower spectrum (as arise in models involving collisional effects in the darksector), while being largely insensitive to a truncation of initial power (asin warm dark matter models). For vanilla cold dark matter (CDM) cosmologies,the summary statistics display strong evolution and redshift-space effects, andare also sensitive to cosmological parameter values for realistic tracersamples. Comparing the VVF of galaxies in the GAMA survey with that ofabundance matched CDM (sub)haloes tentatively reveals environmental effects inGAMA beyond halo mass (modulo unmodelled satellite properties). Our exploratoryanalysis thus paves the way for using the VVF as a new probe of galaxyevolution physics as well as the nature of dark matter and dark energy.

Voronoi volume function: A new probe of cosmology and galaxy evolution