The box within the Universe: anisotropies in periodic cosmological simulations I. Dark-matter-only simulations

Abstract

The vast majority of cosmological simulations employ periodic boundary conditions to achieve statistical homogeneity and to mimic the infinite spatial extent of our Universe. In a cubic periodic domain the Green function breaks full rotational invariance and introduces a geometry-induced anisotropy in the gravitational interaction. We quantify how this intrinsic anisotropy affects cosmic structure growth and investigate the extent to which it biases the commonly used large-scale structure and halo-based observables in dark-matter-only simulations. We analyse an ensemble of 498 cosmological dark-matter-only $N$-body simulations in cubic $T^3$ topological manifolds, evolved to $z=0$, spanning box sizes from $L=6.25\,\mathrm{Mpc}$ to $L=100\,\mathrm{Mpc}$ at fixed mass and force resolution. We compare anisotropy-sensitive statistics across the suite, including the matter power spectrum, halo abundance, merger histories, shapes and alignments, and filament orientations. Finite periodic boundaries imprint orientation-dependent signatures aligned with the box geometry. These signatures propagate beyond the largest modes and can induce systematic shifts in both field-level and halo-level statistics. The detectable effects propagate to scales much smaller than the box size. Our results demonstrate that periodic-box anisotropy is a non-negligible source of systematics for small simulation volumes, including those commonly employed in modern hydrodynamical simulations.