Lovelock and Horndeski theories are diffeomorphism-invariant theories of
gravity with second-order equations of motion. A subset of these
theories can be motivated by effective field theory considerations, and
hence they could describe strong-field deviations from general
relativity. In particular, the effects of some Horndeski theories might
be observable by present and future gravitational wave detectors.

In this talk, I will discuss recent work with Harvey Reall, showing that
these theories admit a locally well-posed initial value formulation at
“weak couplings”. This is achieved by introducing a novel class of
“modified harmonic” gauge conditions and gauge-fixing procedures. If
time allows, I will also discuss methods to construct asymptotically
flat initial data in weakly coupled Lovelock and Horndeski theories
which may be relevant to binary black hole systems.

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