Quadratic DHOST theories revisited

Abstract

We present a novel and remarkably simple formulation of degenerate higher-order scalartensor (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.

Degenerate Hořava gravity

“…time derivatives of the lapse), while still propagating no Ostrogradski ghost. Although similar constructions were already obtained in [15][16][17], here we additionally show that the resulting theory is invariant under spatial diffeomorphisms and a special set of (monotonic) time reparametrizations (which will turn out to be given by 'hyperbolic' time compactifications). While invariance under this special group of transformations is sufficient to determine the form of the kinetic term for the lapse, it does not fix its coefficient unambiguously.…”

“…Therefore, it is possible to realize healthy theories within RFDiff gravity, provided that suitable degeneracy conditions are imposed. These models have been fully classified in [15][16][17], but they may not be very attractive for two reasons. First, the presence of arbitrary functions of N in the Lagrangian results in an infinite number of coupling constants.…”

New constraints on cosmological modified gravity theories from anisotropic three-point correlation functions of BOSS DR12 galaxies

“…This discovery results from a degeneracy between the kinetic terms of the scalar field and the metric. This class of theories has been extended to reach DHOST theories (Langlois & Noui 2016;Crisostomi et al 2016;Ben Achour et al 2016a,b;Langlois 2017;Langlois et al 2020), encompassing Horndeski and Beyond Horndeski theories 8 . So far, DHOST theories have been constrained primarily by three observations 9 : gravitational waves (GW), celestial objects, and cosmological data that is the subject of this paper.…”

Anisotropic cosmological models in Horndeski gravity

“…It is also worth mentioning that, when written in the gauge where G 5 = 0 and hence the condition which insures that the GW speed is equal to the speed of light (in the language of [26] this condition is α 1 = α 2 = 0; see Eq. (D.5) of that work).…”