Higher-derivative operators and effective field theory for general
  scalar-tensor theories
  We discuss the extent to which it is necessary to include higher-derivative
operators in the effective field theory of general scalar-tensor theories. We
explore the circumstances under which it is correct to restrict to second-order
operators only, and demonstrate this using several different techniques, such
as reduction of order and explicit field redefinitions. These methods are
applied, in particular, to the much-studied Horndeski theories. The goal is to
clarify the application of effective field theory techniques in the context of
popular cosmological models, and to explicitly demonstrate how and when
higher-derivative operators can be cast into lower-derivative forms suitable
for numerical solution techniques.
