Significance of void shape: Neutrino mass from Voronoi void halos?

Massive neutrinos suppress the growth of cosmic structure on nonlinear scales, motivating the use of information beyond the power spectrum to tighten constraints on the neutrino mass, for example by considering cosmic voids. It was recently proposed that constraints on neutrino mass from the halo mass function (HMF) can be improved by considering only the halos that reside within voids---the void-halo mass function (VHMF). We extend this analysis, which made spherical assumptions about the shape of voids, to take into account the nonspherical nature of voids as defined by the Voronoi-tessellation-based void finder, VIDE. In turn, after accounting for one spurious nonspherical void, we find no evidence that the VHMF contains information beyond the HMF. Given this finding, we then introduce a novel summary statistic by splitting halos according to the emptiness of their individual environments, defined by the Voronoi cell volume each halo resides in, and combining the mass functions from each split. We name the corresponding statistic the VorHMF and find that it could provide information regarding neutrino mass beyond the HMF. Our work thus motivates the importance of accounting for the full shape of voids in future analyses, both in terms of removing outliers to achieve robust results and as an additional source of cosmological information.