# $\texttt{fRevolution}$ $-$ Relativistic Cosmological Simulations in $f(R)$ Gravity I: Methodology

## TL;DR

The paper introduces $ exttt{fRevolution}$, a new relativistic simulation code for non-linear structure formation in $f(R)$ gravity, extending previous Newtonian approaches with a comprehensive relativistic framework.

## Contribution

It presents the development of a relativistic cosmological simulation code for $f(R)$ gravity, incorporating full gravitational perturbations, which is a novel advancement over existing Newtonian codes.

## Key findings

- Results for point mass fields in $f(R)$ gravity are demonstrated.
- Cosmological simulations in the Hu-Sawicki model are performed and compared to Newtonian codes.
- The code's capabilities are validated through these comparisons.

## Abstract

We present the new relativistic cosmological particle-mesh code $\texttt{fRevolution}$, based on $\texttt{gevolution}$, aimed at simulating non-linear structure formation in $f(R)$ gravity. We introduce the general framework and approximation scheme, and the set of equations used to solve for the full set of gravitational perturbations. We show results for a point mass field and for cosmological simulations in the Hu-Sawicki model, and compare them to those of existing Newtonian codes. A more detailed analysis and discussion of our solutions will be carried out in a following paper.