Void probability function inside cosmic voids: Evidence for hierarchical scaling of high-order correlations in real space

Abstract

We compare the reduced void probability function (VPF) insideãnd outside of cosmic voids in the TNG300-1 simulation, both in realãnd simulated redshift space. The VPF isã special case of the Counts-in-Cellsãpproach for extracting information of high-order clustering that is crucial forã full understanding of the distribution of galaxies. Previous studies have validated the hierarchical scaling paradigm of galaxy clustering moments, in goodãgreement with the 'ne gativ e binomial' model, in redshift surv e ys b ut ha veãlso reported that this paradigm is not valid in real space. Ho we ver, in this work, we find that hierarchical scaling can indeed be found in real space inside cosmic voids. This is well fitted by the ne gativ e binomial model. We find this result to be robustãgainst changes in void identification, galaxy mass, random dilutions,ãnd redshift. Weãlso obtain that the VPF in real spaceãt high redshiftãpproaches the ne gativ e binomial model,ãnd, therefore, it is similar to the VPF inside voidsãt the present time. This study points, for the first time, towards evidence of hierarchical scaling of high-order clustering of galaxies in real space inside voids, preserving the pristine structure formation processes of the Universe.