Compactified Cosmological Simulations of an Infinite Universe

Gábor Rácz1, István Szapudi2, István Csabai1 &László Dobos1

1Department of Physics of Complex Systems, Eötvös Loránd University, 1117 Budapest, Hungary

2Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA


We present a novel N-body method that compactifies the infinite spatial extent of the Universe into a finite sphere with isotropic boundary conditions to simulate the evolution of the large-scale structure. Our approach eliminates the need for periodic boundary conditions, a mere numerical convenience which is not supported by observation and which modifies the law of force on large scales in an unrealistic fashion. We demonstrate that our method outclasses standard simulations executed on workstation-scale hardware in dynamic range, it is balanced in following a comparable number of high and low k modes and, its fundamental geometry and topology match observations. \Moreover, our approach is capable of simulating an expanding, infinite universe in static coordinates with Newtonian dynamics and does not assume a background cosmology to rescale coordinates and velocities. The price of these achievements is that most of the simulated volume has smoothly varying mass and spatial resolution, an approximation that carries different systematics than periodic simulations.

Our initial implementation of the method is called StePS which stands for Stereographically Projected Cosmological Simulations. It uses stereographic projection for space compactification and naive O(N2) force calculation which is nevertheless faster to arrive at a correlation function of the same quality than any standard (tree or P3M) algorithm with similar spatial and mass resolution. The N2 force calculation is easy to adapt to modern graphics cards, hence our code can function as a high-speed prediction tool for modern large-scale surveys. To learn about the limits of the respective methods, we compare StePS with GADGET-2 (Springel, 2005) running matching initial conditions.

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