MG-MAMPOSSt: A code to test modifications of gravity with the dynamics of galaxy clusters

We present an upgraded version of \emph{MG-MAMPOSSt}, a code to constrain modified gravity models with the dynamics of galaxy cluster's members, based on the original \emph{MAMPOSSt} method, along with an application to forecasts. Given an input for the velocity field of member galaxies, the code solves the Jeans' equation to provide a likelihood analysis for the free parameters of the gravity theory, that is, the mass profile and modified gravity parameters. The new version implements two distinct types of gravity modifications, namely general chameleon (including $f(R)$ models) and Beyond Horndeski gravity (Vainshtein screening), and is further equipped with a Monte-Carlo-Markov-Chain module for an efficient parameter space exploration. The program is complemented by the ClusterGEN code, capable of producing mock galaxy clusters under the assumption of spherical symmetry and dynamical equilibrium. The code is written in Fortran and we plan to make it publicly available. Its technical aspects will be presented elsewhere. We demonstrate the potential of the method in an ideal situation by analysing a set of synthetic, isolated and spherically-symmetric dark matter halos, focusing on the statistical degeneracies between model parameters. Assuming the availability of additional lensing-like information, we forecast the constraints on the modified gravity parameters for the two classes of models presented from joint lensing+dynamics analyses in view of upcoming galaxy cluster surveys.