Testing general scalar-tensor gravity and massive gravity with cluster lensing

Understand

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.