Abstract

The pair correlation function (PCF) for galaxies presentstypical oscillations in the range 20-200 Mpc/h which are namedbaryon acoustic oscillation (BAO).We first review and test theoscillations of the PCF when the  2D/3D vertexesof  the Poissonian Voronoi Tessellation (PVT) are considered.We then model the behavior  of the PCF at a small scalein the presence of an auto gravitating  mediumhaving a line/plane of symmetry in 2D/3D.The analysis of the PCF in an astrophysical contextwas split into two,  adopting  a non-PoissonianVoronoi Tessellation (NPVT).We first analyzed the case of a 2D cut which coversfew voids and a 2D cut which covers approximately50 voids.The obtained PCF in the  case of many voidswas then discussedin comparison to thebootstrap predictions fora  PVT  processand the observed PCF for an astronomical catalog.An approximated formula which connects the averaged radius of the cosmicvoids  to the first minimum of the PCF is given.

This work is licensed under a Creative Commons Attribution 4.0 License.