Abstract
Future large-scale spectroscopic astronomical surveys, e.g. Euclid, will enable the compilation of vast new catalogues 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 $M_\nu$ and the dark energy equation of state $w(z) = w_0 + w_a z/(1+z)$. For minimal normal-hierarchy neutrino masses, we forecast that Euclid clusters + voids ideally could reach uncertainties $\sigma(M_\nu) \lesssim 15$ meV, $\sigma(w_0) \lesssim~0.02$, $\sigma(w_a) \lesssim 0.07$, 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 $\gtrsim 99\%$ confidence.
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