Effective Description of HigherOrder ScalarTensor Theories
(34 pages)

The EFT of dark energy is extended to include time derivatives of the
lapse, which had previously been ommitted because they generically
propagate an additional scalar dof, but here they are included in such a
way that the resulting Lagrangian is degenerate (c.f. DHOST theories).
Linear perturbations about Minkowski and FRW can only obey a Poissonlike
equation in the static limit in the beyond Horndeski theories.

This new EFT encapsulates not only Horndeski, but also the ghostfree
higher derivative scalar field theories, known as DHOST (which includes the
`beyond Horndeski' theories). Elsewhere it has been shown that Lorentz
invariance and no strong coupling in the tensor sector restricts one to
theories which are field redefinable to Horndeski. This work suggests that
to reproduce Poissonlike cosmological behaviour, one is similarly
restricted to Horndeski (or beyondHorndeski) theory.
