Testing Void Linearity using the Zel’Dovich Approximation

In this study, we investigate voids, which are regions of low density within the cosmic web, which provide valuable insights into cosmological evolution and can help constrain cosmological parameters. To identify voids, we utilize simulations with both normal and inverted initial conditions and employ the Zel’dovich approximation, a first-order Lagrangian perturbation theory that simplifies the evolution of density fluctuations by assuming matter moves along straight lines. The initial conditions are generated by the \verb|GenetIC| \citep{Stopyra2021a} algorithm and the simulations are evolved using \verb|GADGET2| \citep{Springel2005} with dark matter only. By mapping the halos from the inverted simulation onto the normal simulation, we effectively detect voids in the normal simulation. Our analysis reveals a high degree of correspondence between Zel'dovich and full N-body voids and halos, especially when comparing power spectra and autocorrelation functions, suggesting a promising method for void cataloguing. However, some discrepancies are observed which raise questions about the suitability of the Zel’dovich model for accurately describing void evolution and, notably, testing void linearity.