Quadratic DHOST theories revisited

TL;DR

This paper introduces a new geometric formulation of quadratic DHOST theories, simplifying their classification by using disformal transformations to relate them to familiar geometric quantities.

Contribution

It presents a novel, simple geometric reformulation of quadratic DHOST theories, clarifying their classification and relation to scalar-tensor theories through disformal transformations.

Findings

Lagrangian reduces to Einstein-Hilbert plus geometric terms in a special frame

Classification of quadratic DHOST theories becomes more transparent

Applicable to scalar-tensor theories degenerate in the unitary gauge

Abstract

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