MG-MAMPOSSt: A code to test modifications of gravity with the dynamics
  of galaxy clusters
  We present an upgraded version of \textsc{MG-MAMPOSSt}, an extension of the
\textsc{MAMPOSSt} algorithm that performs Bayesian fits of models of mass and
velocity anisotropy profiles to the distribution of tracers in projected phase
space, to handle modified gravity models and constrain their parameters. The
new version implements two distinct types of gravity modifications, namely
general chameleon and 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 \textsc{ClusterGEN} code, capable of
producing mock galaxy clusters under the assumption of spherical symmetry,
dynamical equilibrium, and Gaussian local velocity distribution functions as in
\textsc{MAMPOSSt}. We demonstrate the potential of the method by analysing a
set of synthetic, isolated spherically-symmetric dark matter haloes, 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 models presented, as
expected from joint lensing+internal kinematics analyses, in view of upcoming
galaxy cluster surveys. In Vainshtein screening, we forecast the weak lensing
effect through the estimation of the full convergence-shear profile. For
chameleon screening, we constrain the allowed region in the space of the two
free parameters of the model, further focusing on the $f(\mathcal{R})$ subclass
to obtain realistic bounds on the background field $|f_{\mathcal{R}0}|$. Our
analysis demonstrates the complementarity of internal kinematics and lensing
probes for constraining modified gravity theories, and how the bounds on
Vainshtein-screened theories improve through the combination of the two probes.
