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

TL;DR

This paper compares Yukawa and Newtonian gravitational forces in a cubic simulation box, identifying scales where deviations occur and analyzing the effects of boundary conditions on force behavior.

Contribution

It provides a detailed analysis of gravitational force deviations in cosmological simulations, highlighting the impact of boundary conditions and force laws.

Findings

Deviations from Yukawa law occur at specific scales in periodic boxes.

Boundary conditions significantly affect gravitational force calculations.

Newtonian approximation remains valid within certain physical scales.

Abstract

We study the behaviour of Yukawa and Newtonian gravitational forces in a cubic box with fully periodic boundaries commonly encountered in N-body simulations of the structure formation. Placing a single gravitating body at the origin of coordinates, we reveal the scales at which non-negligible deviation from the Yukawa law occurs when the Newtonian approximation is employed. We discuss the results in terms of the corresponding physical distances today as well as earlier, back at the matter-dominated stage. Revisiting the problem for free boundaries, we also compare the periodic and plain gravitational forces for Yukawa-type interactions.