Constraining cosmological parameters using void statistics from the SDSS survey

We identify voids as maximal non-overlapping spheres within the haloes of the Uchuu simulation and three smaller halo simulation boxes with smaller volume and different $\sigma_{8}$ values, and galaxies with redshift in the range $0.02<z<0.132$ and absolute magnitude in the $r-$band $M_{r}<-20.5$ of 32 Uchuu-SDSS simulated lightcones the seventh release of \textit{The Sloan Digital Sky Survey} (SDSS DR7) survey. We compute the Void Probability Function and the abundance of voids larger than $r$ predicted by the theoretical framework used in this work and we check that it predicts successfully both void functions for the halo simulation boxes. Next, we asses the potential of this theoretical framework to constrain cosmological parameters using Uchuu-SDSS void statistics, and we calculate the confidence levels using Monte Carlo Markov Chain techniques to infer the values of $\sigma_{8}$, $\Omega_{\rm m}$ and H$_{0}$ from the SDSS sample used. The constraints we obtain from the SDSS survey sample used. The results are: $\sigma_{8}=1.028^{+0.273}_{-0.305}$, $\Omega_{\rm m}=0.296^{+0.110}_{-0.102}$, H$_{0}=83.43\pm^{+29.27}_{-27.70}$, $\Gamma=0.1947^{+0.0578}_{-0.0516}$ and S$_{8}$=1.017$^{+0.363}_{-0.359}$. If we combine these constraints with KiDS-1000+DESY3, we get $\sigma_{8}=0.858^{+0.040}_{-0.040}$, $\Omega_{\rm m}=0.257\pm^{+0.023}_{-0.020}$, H$_{0}=74.17^{+4.66}_{-4.66}$ and S$_{8}$=0.794$^{+0.016}_{-0.016}$. The combined uncertainties are approximately a factor 2-3 smaller than only-Weak-Lensing uncertainties. This is a consequence of the orientation of the confidence level contours of SDSS voids and Weak Lensing in the plane $\sigma_{8}-\Omega_{\rm m}$, which are almost orthogonal (abridged).