The Hidden Role of Anisotropies in Shaping Structure Formation in Cosmological N-Body Simulations

Abstract

Initial conditions in cosmological $N$-body simulations are typically generated by displacing particles from a regular cubic lattice using a correlated field derived from the linear power spectrum, often via the Zel'dovich approximation. While this procedure reproduces the target two-point statistics (e.g., the power spectrum or correlation function), it introduces subtle anisotropies due to the underlying lattice structure. These anisotropies, invisible to angle-averaged diagnostics, become evident through directional measures such as the Angular Distribution of Pairwise Distances. Analyzing two Cold Dark Matter simulations with { varying resolutions and box sizes}, we show that these anisotropies are not erased but are amplified by gravitational evolution. They seed filamentary structures that persist into the linear regime, remaining visible even at redshift $z=0$. Our findings demonstrate that such features are numerical artifacts -- emerging from the anisotropic coupling between the displacement field and the lattice -- not genuine predictions of an isotropic cosmological model. These results underscore the importance of critically reassessing how initial conditions are constructed, particularly when probing the large-scale, quasi-linear regime of structure formation.

arXiv comment22 pages, 18 figures. Revised version to appear in Physical Review D

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