Cluster-Void Degeneracy Breaking: Dark Energy, Planck and the Largest Cluster & Void

Abstract

Combining galaxy cluster and void abundances breaks the degeneracy between mean matter density ${\Omega }_{\mathrm{m}}$ and power spectrum normalization ${\sigma }_8$. In a first for voids, we constrain ${\Omega }_{\mathrm{m}}=0.21\pm 0.10$ and ${\sigma }_8=0.95\pm 0.21$ for a flat $\Lambda$CDM universe, using extreme-value statistics on the claimed largest cluster and void. The Planck-consistent results detect dark energy with two objects, independently of other dark energy probes. Cluster-void studies also offer complementarity in scale, density, and non-linearity - of particular interest for testing modified-gravity models.

arXiv comment13 pages, 1 figure, 2 tables. ApJL accepted, revised version. Minor changes: added clarifying remarks, discussion on redshift sensitivity and more general models. Results and conclusions unchanged

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