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-v and the dark energy equation of state state w(z) = w(0) + w(a)z/(1 + z). For minimal normalhierarchy neutrino masses, we forecast that Euclid clusters+voids ideally could reach uncertainties sigma(M-v) less than or similar to 15 meV, sigma(w(0))less than or similar to 0.02,sigma(w(a))less than or similar to 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 greater than or similar to 99% confidence.