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We present the first cosmological constraints derived from the analysis ofthe void size function. This work relies on the final BOSS DR12 data set, alarge spectroscopic galaxy catalog, ideal for the identification of cosmicvoids. We extract a sample of voids from the distribution of galaxies and weapply a cleaning procedure aimed at reaching high levels of purity andcompleteness. We model the void size function by means of an extension of thepopular volume-conserving model, based on two additional nuisance parameters.Relying on mock catalogs specifically designed to reproduce the BOSS DR12galaxy sample, we calibrate the extended size function model parameters andvalidate the methodology. We then apply a Bayesian analysis to constrain the$\Lambda$CDM model and one of its simplest extensions, featuring a constantdark energy equation of state parameter, $w$. Following a conservativeapproach, we put constraints on the total matter density parameter and theamplitude of density fluctuations, finding $\Omega_{\rm m}=0.29 \pm 0.06$ and$\sigma_8=0.79^{+0.09}_{-0.08}$. Testing the alternative scenario, we derive$w=-1.1\pm 0.2$, in agreement with the $\Lambda$CDM model. These results areindependent and complementary to those derived from standard cosmologicalprobes, opening up new ways to identify the origin of potential tensions in thecurrent cosmological paradigm.

Cosmological constraints from the BOSS DR12 void size function