Cluster-Void Degeneracy Breaking: Modified Gravity in the Balance

Combining galaxy cluster and void abundances is a novel, powerful way to constrain deviations from General Relativity and the $\mathrm{\Lambda }$CDM model. For a flat $w$CDM model with growth of large-scale structure parameterized by the redshift-dependent growth index $\gamma (z)={\gamma }_0+{\gamma }_{1}z\mathrm{/}(1+z)$ of linear matter perturbations, combining void and cluster abundances in future surveys with Euclid and the 4-metre Multi-Object Spectroscopic Telescope (4MOST) could improve the Figure of Merit for ($w,{\gamma }_0,{\gamma }_1$) by a factor of 20 compared to individual abundances. In an ideal case, improvement on current cosmological data is a Figure of Merit factor $600$ or more.