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We present a novel parameter-free cosmological void finder (\textsc{dive},Delaunay TrIangulation Void findEr) based on Delaunay Triangulation (DT), whichefficiently computes the empty spheres constrained by a discrete set oftracers. We define the spheres as DT voids, and describe their properties,including an universal density profile together with an intrinsic scatter. Weapply this technique on 100 halo catalogues with volumes of 2.5\,$h^{-1}$Gpcside each, with a bias and number density similar to the BOSS CMASS LuminousRed Galaxies, performed with the \textsc{patchy} code. Our results show thatthere are two main species of DT voids, which can be characterised by theradius: they have different responses to halo redshift space distortions, tonumber density of tracers, and reside in different dark matter environments.Based on dynamical arguments using the tidal field tensor, we demonstrate thatlarge DT voids are hosted in expanding regions, whereas the haloes used toconstruct them reside in collapsing ones. Our approach is therefore able toefficiently determine the troughs of the density field from galaxy surveys, andcan be used to study their clustering. We further study the power spectra of DTvoids, and find that the bias of the two populations are different,demonstrating that the small DT voids are essentially tracers of groups ofhaloes.

DIVE in the cosmic web: voids with Delaunay Triangulation from discrete matter tracer distributions