The anisotropy of the power spectrum in periodic cosmological simulations

Abstract

The classical gravitational force on a torus is anisotropic and always lower than Newton's 1/r 2 law. We demonstrate the effects of periodicity in dark matter only N-body simulations of spherical collapse and standard ΛCDM initial conditions. Periodic boundary conditions cause an overall negative and anisotropic bias in cosmological simulations of cosmic structure formation. The effect is most significant when the largest mildly non-linear scales are comparable to the linear size of the simulation box, as often is the case for high-resolution hydrodynamical simulations. Spherical collapse morphs into a shape similar to an octahedron. The anisotropic growth distorts the large-scale ΛCDM dark matter structures. We introduce the direction-dependent power spectrum invariant under the octahedral group of the simulation volume and show that the results break spherical symmetry.

Yukawa vs. Newton: gravitational forces in a cubic cosmological simulation box

“…As for the plain Yukawa vs. Yukawa-Ewald forces, the corresponding distances are revealed to be 18 and 38 Mpc, respectively. The measure of discrepancy between the plain Newtonian and periodic Newton-Ewald forces has previously been studied in view of cosmological simulations [1,14], with a reported relative error of 10 −5 produced at distances as small as 1% of the box size [1]. Here we have shown that the error associated with different laws of gravitation, i.e.…”

“…Given the possibility that periodicity may not be demanded by topology, and hence the related effects in simulations may be artificial [14], we find it worthwhile to study two laws of gravity also for free boundaries. Losing the lattice, we formulate the solutions again for a single gravitating body, placed at (x, y, z) = (0, 0, 0).…”