# Voronoi chords in flat cosmology

## TL;DR

This paper develops formulas for chord length distributions in Voronoi tessellations, incorporating a scale parameter to model cosmic voids, and compares these models with galaxy catalog observations.

## Contribution

It introduces new formulas for chord distributions in Poissonian and non-Poissonian Voronoi tessellations with a scale parameter for cosmic voids.

## Key findings

- Theoretical distributions match observed cosmic voids in galaxy catalogs.
- Graphical comparisons validate the Voronoi models.
- Models effectively incorporate cosmic void scale parameters.

## Abstract

In this paper we present formulae for chord length distribution in the framework of Poissonian Voronoi Tessellation (PVT) and non Poissonian Voronoi Tessellation (NPVT). The introduction of the scale parameter in the obtained distributions allows us to model the chord for cosmic voids. A graphical comparison between cosmic voids visible on two catalogs of galaxies, 2dFGRS and VIPERS, and theoretical random chords is reported.