Abstract
We aim to constrain the amplitude of the linear spectrum of density fluctuations (σ_8), the matter density parameter (Ω_ m), the Hubble constant (H_0) c h, and S_8 from Sloan Digital Sky Survey Data Release 7 (SDSS DR7) by studying the abundance of large voids in the large-scale structure of galaxies. Voids are identified as maximal non-overlapping spheres within SDSS DR7 galaxies with redshifts of $0.02<z<0.132$ and absolute magnitudes of M_ r <-20.5. We used the theoretical framework developed in previous works and recalibrated the data using halo simulations to constrain σ_8, Ω_ m, and H_0 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. We have proven that the theoretical framework recovers σ_8, Ω_ m, and H_0 values from the halo simulation boxes for different values of σ_8 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: Ω_ m H_ Γ=0.270^ and S_ . Combining these constraints with the Kilo Degree Survey (KiDS-1000) and the Dark Energy Survey (DESY3) yields σ_ Ω_ m H_ and S_ . The combined uncertainties of σ_8 and Ω_ m 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 -Ω_ m plane.
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