Quadratic DHOST theories revisited
arXiv:2012.10218 · doi:10.1103/PhysRevD.103.084022
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.
16 pages (9 pages + Appendix)
References in corpus (33)
- GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
- The galileon as a local modification of gravity
- Generalized G-inflation: Inflation with the most general second-order field equations
- From k-essence to generalised Galileons
- Healthy theories beyond Horndeski
- Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability
- Effective Field Theory for Inflation
- Transforming gravity: from derivative couplings to matter to second-order scalar-tensor theories beyond the Horndeski Lagrangian
- Exploring gravitational theories beyond Horndeski
- Dressing a black hole with a time-dependent Galileon
- Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order
- Essential Building Blocks of Dark Energy
- Extended Scalar-Tensor Theories of Gravity
- Models of non-relativistic quantum gravity: the good, the bad and the healthy
- Degenerate higher order scalar-tensor theories beyond Horndeski and disformal transformations
- Dark Energy and Modified Gravity in Degenerate Higher-Order Scalar-Tensor (DHOST) theories: a review
- Scalar-tensor theories and modified gravity in the wake of GW170817
- Gravitational Rainbows: LIGO and Dark Energy at its Cutoff
- A unifying description of dark energy
- Hamiltonian analysis of higher derivative scalar-tensor theories
- Unifying framework for scalar-tensor theories of gravity
- Effective Description of Higher-Order Scalar-Tensor Theories
- Vainshtein mechanism after GW170817
- Gravitational Wave Decay into Dark Energy
- Horndeski: beyond, or not beyond?
- Hamiltonian analysis of spatially covariant gravity
- "Shadowy" modes in Higher-Order Scalar-Tensor theories
- Ostrogradsky in Theories with Multiple Fields
- General Relativity solutions with stealth scalar hair in quadratic higher-order scalar-tensor theories
- Spatially covariant gravity with velocity of the lapse function: the Hamiltonian analysis
- Reconsidering the Ostrogradsky theorem: Higher-derivatives Lagrangians, Ghosts and Degeneracy
- Tracker and scaling solutions in DHOST theories
- Late time cosmological evolution in DHOST models
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- Higher Derivative Scalar Tensor Theory in Unitary Gauge
- Stars disformally coupled to a shift-symmetric scalar field
- Recent Developments in Degenerate Higher Order Scalar Tensor Theories
- Cosmic evolution in DHOST theories with scaling solutions