Quadratic degenerate higher-order scalar-tensor theories revisited

We present a novel and remarkably simple formulation of degenerate higher-order scalar-tensor (DHOST) theories whose Lagrangian is quadratic in second derivatives some scalar field. Using disformal transformations the metric, we identify special "frame" (or metric) for which DHOST reduces to usual Einstein-Hilbert term plus few terms that depend on geometric quantities characterizing uniform field hypersurfaces. In particular, physically interesting class Ia, simply consists proportional three-dimensional curvature The classification all becomes particularly transparent this reformulation, also applies are only unitary gauge.