Simulation techniques for modified gravity

TL;DR

This paper reviews simulation techniques for modified gravity theories in cosmology, emphasizing numerical methods like multigrid to solve complex equations and discussing extensions beyond static approximations and baryonic effects.

Contribution

It provides a comprehensive classification of numerical challenges in simulating modified gravity and details specific multigrid techniques tailored for these models.

Findings

Multigrid methods are effective for solving elliptic equations in MG simulations.

Extensions beyond static approximation improve simulation accuracy.

Handling baryons introduces additional complexity in MG simulations.

Abstract

The standard paradigm of cosmology assumes General Relativity (GR) is a valid theory for gravity at scales in which it has not been properly tested. Developing novel tests of GR and its alternatives is crucial if we want to give strength to the model or find departures from GR in the data. Since alternatives to GR are usually defined through nonlinear equations, designing new tests for these theories implies a jump in complexity and thus, a need for refining the simulation techniques. We summarize existing techniques for dealing with modified gravity (MG) in the context of cosmological simulations. $N$-body codes for MG are usually based on standard gravity codes. We describe the required extensions, classifying the models not according to their original motivation, but by the numerical challenges that must be faced by numericists. MG models usually give rise to elliptic equations, for which multigrid techniques are well suited. Thus, we devote a large fraction of this review to describing this particular technique. Contrary to other reviews on multigrid methods, we focus on the specific techniques that are required to solve MG equations and describe useful tricks. Finally, we describe extensions for going beyond the static approximation and dealing with baryons.