Cluster-void degeneracy breaking: Neutrino properties and dark energy

Future large-scale spectroscopic astronomical surveys, e. g. , Euclid, will enable the compilation of vast new catalogs of clusters and voids in the galaxy distribution. By combining the constraining power of both cluster and void number counts, such surveys could place stringent simultaneous limits on the sum of neutrino masses M_ and the dark energy equation of state w (z) =w₀+w₀z/ (1+z). For minimal normal-hierarchy neutrino masses, we forecast that Euclid clusters+voids ideally could reach uncertainties (M_) 15 meV, (w₀) 0. 02, (w₀) 0. 07, independent of other data. Such precision is competitive with expectations for, e. g. , galaxy clustering and weak lensing in future cosmological surveys and could reject an inverted neutrino mass hierarchy at 99% confidence.