Testing general scalar-tensor gravity and massive gravity with cluster
  lensing
  We explore the possibility of testing modified gravity exhibiting the
Vainshtein mechanism against observations of cluster lensing. We work in the
most general scalar-tensor theory with second-order field equations
(Horndeski's theory), and derive static and spherically symmetric solutions,
for which the scalar field is screened below a certain radius. It is found that
the essential structure of the problem in the most general case can be captured
by the program of classifying Vainshtein solutions out of different solutions
to a quintic equation, as has been performed in the context of massive gravity.
The key effect on gravitational lensing is that the second derivative of the
scalar field can substantially be large at the transition from screened to
unscreened regions, leaving a dip in the convergence. This allows us to put
observational constraints on parameters characterizing the general
scalar-tensor modification of gravity. We demonstrate how this occurs in
massive gravity as an example, and discuss its observational signatures in
cluster lensing.
