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

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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.