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 σ₈ values, and galaxies with redshift in the range $0.02<z<0.132$ and absolute magnitude in the $r-$band Mᵣ<-20.5 of 32 Uchuu-SDSS simulated lightcones the seventh release of 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 σ₈, Ωₘ and H₀ from the SDSS sample used. The constraints we obtain from the SDSS survey sample used. The results are: σ₈=1.028+0.273-0.305, Ωₘ=0.296+0.110-0.102, H₀=83.43±+29.27-27.70, Γ=0.1947+0.0578-0.0516 and S₈=1.017+0.363-0.359. If we combine these constraints with KiDS-1000+DESY3, we get σ₈=0.858+0.040-0.040, Ωₘ=0.257±+0.023-0.020, H₀=74.17+4.66-4.66 and S₈=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 σ₈-Ωₘ, which are almost orthogonal (abridged).