  We introduce the LOCal Universe Screening Test Suite (LOCUSTS) project, an
effort to create 'screening maps' in the nearby Universe to identify regions in
our neighbourhood which are screened, i.e., regions where deviations from
General Relativity (GR) are suppressed, in various modified gravity (MG)
models. In these models, deviations from the GR force law are often stronger
for smaller astrophysical objects, making them ideal test beds of gravity in
the local Universe. However, the actual behaviour of the modified gravity force
also depends on the environment of the objects, and to make accurate
predictions one has to take the latter into account. This can be done
approximately using luminous objects in the local Universe as tracers of the
underlying dark matter field. Here, we propose a new approach that takes
advantage of state-of-the-art Bayesian reconstruction of the mass distribution
in the Universe, which allows us to solve the modified gravity equations and
predict the screening effect more accurately. This is the first of a series of
works, in which we present our methodology and some qualitative results of
screening for a specific MG model, $f(R)$ gravity. Applications to test models
using observations and extensions to other classes of models will be studied in
future works.
