Non-linear evolution of f(R) cosmologies I: methodology

TL;DR

This paper presents a new computational method for simulating f(R) gravity models in cosmology, enabling the study of their effects on structure formation and gravitational dynamics without conflicting with solar system tests.

Contribution

It introduces an efficient numerical approach using a Newton-Gauss-Seidel relaxation with multigrid to solve the non-linear Poisson equation in f(R) cosmologies, validated through various tests.

Findings

f(R) models enhance the dark matter power spectrum by ~20%

The method accurately reproduces analytical solutions and collapse tests

Simulations show stronger gravity effects in f(R) cosmologies

Abstract

We introduce the method and the implementation of a cosmological simulation of a class of metric-variation f(R) models that accelerate the cosmological expansion without a cosmological constant and evade solar-system bounds of small-field deviations to general relativity. Such simulations are shown to reduce to solving a non-linear Poisson equation for the scalar degree of freedom introduced by the f(R) modifications. We detail the method to efficiently solve the non-linear Poisson equation by using a Newton-Gauss-Seidel relaxation scheme coupled with multigrid method to accelerate the convergence. The simulations are shown to satisfy tests comparing the simulated outcome to analytical solutions for simple situations, and the dynamics of the simulations are tested with orbital and Zeldovich collapse tests. Finally, we present several static and dynamical simulations using realistic cosmological parameters to highlight the differences between standard physics and f(R) physics. In general, we find that the f(R) modifications result in stronger gravitational attraction that enhances the dark matter power spectrum by ~20% for large but observationally allowed f(R) modifications. More detailed study of the non-linear f(R) effects on the power spectrum are presented in a companion paper.