  We introduce a new scheme based on the marked correlation function to probe
gravity using the large-scale structure of the Universe. We illustrate our
approach by applying it to simulations of the metric-variation $f(R)$ modified
gravity theory and general relativity (GR). The modifications to the equations
in $f(R)$ gravity lead to changes in the environment of large-scale structures
that could, in principle, be used to distinguish this model from GR. Applying
the Monte Carlo Markov Chain algorithm, we use the observed number density and
two-point clustering to fix the halo occupation distribution (HOD) model
parameters and build mock galaxy catalogues from both simulations. To generate
a mark for galaxies when computing the marked correlation function we estimate
the local density using a Voronoi tessellation. Our approach allows us to
isolate the contribution to the uncertainty in the predicted marked correlation
function that arises from the range of viable HOD model parameters, in addition
to the sample variance error for a single set of HOD parameters. This is
critical for assessing the discriminatory power of the method. In a companion
paper we apply our new scheme to a current large-scale structure survey.
