Constraining cosmological parameters using void statistics from the SDSS survey

Aims. We aim to constrain the amplitude of the linear spectrum of density fluctuations (σ8), the matter density parameter (Ωm), the Hubble constant (H0), Γ = Ωch, and S8 from Sloan Digital Sky Survey Data Release 7 (SDSS DR7) by studying the abundance of large voids in the large-scale structure of galaxies. Methods. Voids are identified as maximal non-overlapping spheres within SDSS DR7 galaxies with redshifts of 0.02 < z < 0.132 and absolute magnitudes of Mr < −20.5. We used the theoretical framework developed in previous works and recalibrated the data using halo simulations to constrain σ8, Ωm, and H0 from the sample of SDSS galaxies mentioned above using a Bayesian analysis and Markov chain Monte Carlo (MCMC) technique. This method has also been validated using simulated halo boxes and galaxy lightcones. Results. We have proven that the theoretical framework recovers σ8, Ωm, and H0 values from the halo simulation boxes for different values of σ8 within 1σ (2σ) in real (redshift) space. The theoretical framework void statistics from mock lightcones shows significant potential: we have studied the marginalised posteriors in each plane and checked that we were able to recover Planck values for the all the parameters. The results we obtained from the SDSS sample are: $ \sigma_{8}=1.520^{+0.416}_{-0.441} $, $ \Omega_{\mathrm{m}}=0.459^{+0.184}_{-0.184} $, H$ _{0}=71.63^{+12.60}_{-11.77} $, $ \Gamma=0.270^{+0.094}_{-0.100} $, and S$ _{8}=1.87^{+0.59}_{-0.76} $. Combining these constraints with the Kilo Degree Survey (KiDS-1000) and the Dark Energy Survey (DESY3) yields $ \sigma_{8}=0.858^{+0.040}_{-0.040} $, $ \Omega_{\mathrm{m}}=0.257^{+0.023}_{-0.020} $, H$ _{0}=74.17^{+4.66}_{-4.66} $, and S$ _{8}=0.794^{+0.016}_{-0.016} $. The combined uncertainties of σ8 and Ωm have been reduced by a factor of 2-3, compared to KiDS-100+DESY3 alone, due to the nearly orthogonal marginalised posteriors of SDSS voids and weak lensing in the σ8 − Ωm plane.