Cylindrical cosmological simulations with STEPS

¹ Department of Physics, University of Helsinki, Gustaf Hällströmin katu 2, FI-00014 Helsinki, Finland
² Department of Physics of Complex Systems, Eötvös Loránd University, Budapest, Hungary
³ Institute for Particle and Nuclear Physics, HUN-REN Wigner Research Centre for Physics, Budapest, Hungary
⁴ Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 20 February 2026
Accepted: 30 April 2026

Abstract

Context. The global topology of the Universe can affect long-range gravitational forces via boundary conditions. Detailed studies of non-trivial topologies require simulations that natively adopt such geometries. Cosmological N-body simulations typically evolve matter in a periodic cubic box. While numerically convenient, this imposes a non-trivial three-torus topology that affects long-range gravitational forces, potentially biasing large-scale statistics.

Aims. We introduce a compactified simulation framework that is only periodic along a single axis, characterised by an infinite topology with isotropic boundary conditions towards the perpendicular directions, namely, a S¹ × ℝ² (slab) topology. This new simulation geometry is ideal for simulating systems with cylindrical symmetries such as filaments or certain anisotropic cosmological models.

Methods. We compactified the comoving space via an inverse stereographic projection along the radial direction of a periodic cylinder. Then, we evolved the particles based on Newtonian dynamics. A smoothly varying spatial and mass resolution with radius suppresses edge artefacts at the free outer boundary. Our implementation in the StePS (STEreographically Projected cosmological Simulations) framework uses a direct 𝒪(N²) force calculation that maps efficiently to GPUs, as well as an Octree 𝒪(N log N) force calculation for use on large CPU clusters.

Results. The cylindrical domain’s topology enables fully self-consistent simulations to be run in the S¹ × ℝ² manifold, while mitigating any periodic-image artefacts with respect to targets whose symmetries are mismatched to a cubic box. The main trade-off is a radially varying resolution with distinct systematics and analysis requirements. Finally, we demonstrate the accuracy of the new simulation method via a standard lambda cold dark matter (ΛCDM) cosmological simulation.