Strong gravitational lensing in Horndeski theory of gravity

In this paper we build the general gravitational-lensing formalism for luminal Horndeski theories, deriving the Jacobi matrix equation and the general angular diameter distance in these theories through the screen-space formalism. We generalize the focusing and multiple-lensing theorems in General Relativity to include the luminal Horndeski theories and derive constraints they must satisfy to exhibit the same gravitional-lensing behavior in General Relativity. This provides a way to test theories through strong -lensing effects, as well as a full theoretical framework for testing lensing predictions in these theories against observations. We find that for some theories, like metric f(R) and unified k -essence, the obtained theorems are satisified in general physical cases, while for others, like Galileon condensate models, the current observational constraints show the theory has the same gravitational-lensing behavior as in General Relativity.