Spatial correlations of extended cosmological structures

Studies of large-scale structures in the Universe, such as superstructures or cosmic voids, have been widely used to characterize the properties of the cosmic web through statistical analyses. On the other hand, the 2-point correlation function of large-scale tracers such as galaxies or halos provides a reliable statistical measure. However, this function applies to the spatial distribution of point-like objects, and therefore it is not appropriate for extended large structures which strongly depart from spherical symmetry. Here we present an analysis based on the standard correlation function formalism that can be applied to extended objects exhibiting arbitrary shapes. Following this approach, we compute the probability excess $Ξ$ of having spheres sharing parts of cosmic structures with respect to a realization corresponding to a distribution of the same structures in random positions. For this aim, we identify superstructures defined as Future Virialized Structures (FVSs) in semi-anaytic galaxies on the MPDL2 MultiDark simulation. We have also identified cosmic voids to provide a joint study of their relative distribution with respect to the superstructures. Our analysis suggests that $Ξ$ provides useful characterizations of the large scale distribution, as suggested from an analysis of sub-sets of the simulation. Even when superstructure properties may exhibit negligible variations across the sub-sets, $Ξ$ has the sensitivity to statistically distinguish sub-boxes that departs from the mean at larger scales. Thus, our methods can be applied in analysis of future surveys to provide characterizations of large-scale structure suitable to distinguish different theoretical scenarios.