Abstract
We constrain the viable models of Horndeski gravity, written in its equivalent Generalised Galileon version, by resorting to the Witten positive energy theorem. We find that the free function G 3(ϕ,X) in the Lagrangian is constrained to be a function solely of the scalar field, G 3(ϕ), and relations among the free functions are found. Other criterion for stability are also analysed, such as the attractiveness of gravity, and the Dolgov-Kawasacki instability. Some applications for cosmology are discussed.
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