Exploring the cosmological synergy between galaxy cluster and cosmic void number counts

Galaxy clusters and cosmic voids, the most extreme objects of our Universe in terms mass size, trace two opposite sides large-scale matter density field. By studying their abundance as a function radius, respectively, i.e. halo (HMF) void size (VSF), it is possible to achieve fundamental constraints on cosmological model. While HMF has already been extensively exploited providing robust main model parameters (e.g. $\Omega_{\rm m}$, $\sigma_8$ $S_8$), VSF still emerging viable effective probe. Given expected complementarity these statistics, this work we aim at estimating costraining power deriving from combination. To end, exploit realistic mock samples galaxy voids extracted state-of-the-art large hydrodynamical simulations, redshift range $0.2 \leq z 1$. We perform an accurate calibration free models, needed take into account differences between types tracers used those considered previous literature analyses. Then, obtain m}$ by performing Bayesian analysis. find that cluster counts represent powerful independent complementary probes test framework. In particular, constraining improves drastically with contribution, increasing $S_8$ constraint precision factor about 60%.