Speeding up $N$-body simulations of modified gravity: Chameleon screening models

TL;DR

The paper introduces a new, efficient numerical method for simulating modified gravity theories like $f(R)$ models, significantly reducing computational time and enabling high-resolution, large-scale cosmological simulations.

Contribution

A novel analytical solution-based numerical method that accelerates $f(R)$ gravity simulations, overcoming convergence issues of traditional iterative algorithms.

Findings

Simulation speed increased by up to 20 times.

Enabled high-resolution, large-volume simulations previously computationally prohibitive.

Facilitated large ensemble runs for covariance analysis in cosmology.

Abstract

We describe and demonstrate the potential of a new and very efficient method for simulating certain classes of modified gravity theories, such as the widely studied $f(R)$ gravity models. High resolution simulations for such models are currently very slow due to the highly nonlinear partial differential equation that needs to be solved exactly to predict the modified gravitational force. This nonlinearity is partly inherent, but is also exacerbated by the specific numerical algorithm used, which employs a variable redefinition to prevent numerical instabilities. The standard Newton-Gauss-Seidel iterative method used to tackle this problem has a poor convergence rate. Our new method not only avoids this, but also allows the discretised equation to be written in a form that is analytically solvable. We show that this new method greatly improves the performance and efficiency of $f(R)$ simulations. For example, a test simulation with $512^3$ particles in a box of size $512 \, \mathrm{Mpc}/h$ is now 5 times faster than before, while a Millennium-resolution simulation for $f(R)$ gravity is estimated to be more than 20 times faster than with the old method. Our new implementation will be particularly useful for running very high resolution, large-sized simulations which, to date, are only possible for the standard model, and also makes it feasible to run large numbers of lower resolution simulations for covariance analyses. We hope that the method will bring us to a new era for precision cosmological tests of gravity.