Higher Derivative Scalar Tensor Theory in Unitary Gauge
arXiv:2111.11791 · doi:10.1088/1475-7516/2022/03/022
Abstract
Ostrogradsky instability generally appears in nondegenerate higher-order derivative theories and this issue can be resolved by removing any existing degeneracy present in such theories. We consider an action involving terms that are at most quadratic in second derivatives of the scalar field and non-minimally coupled with the curvature tensors. We perform a 3+1 decomposition of the Lagrangian to separate second-order time derivative terms from rest. This decomposition is useful for checking the degeneracy hidden in the Lagrangian and helps us find conditions under which Ostrogradsky instability does not appear. We show that our construction of Lagrangian resembles that of a GR-like theory for a particular case in the unitary gauge. As an example, we calculate the equation of motion for the flat FRW. We also write the action for open and closed cases, free from higher derivatives for a particular choice derived from imposing degeneracy conditions.
15 pages, 0 figures
References in corpus (18)
- Quantum Gravity at a Lifshitz Point
- The Effective Field Theory of Inflation
- Dark Energy after GW170817: dead ends and the road ahead
- Strong constraints on cosmological gravity from GW170817 and GRB 170817A
- Implications of the Neutron Star Merger GW170817 for Cosmological Scalar-Tensor Theories
- Healthy theories beyond Horndeski
- Horndeski theory and beyond: a review
- Starting the Universe: Stable Violation of the Null Energy Condition and Non-standard Cosmologies
- Exploring gravitational theories beyond Horndeski
- Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order
- Cuscuton: A Causal Field Theory with an Infinite Speed of Sound
- Unifying framework for scalar-tensor theories of gravity
- Cuscuton Cosmology: Dark Energy meets Modified Gravity
- Hamiltonian analysis of spatially covariant gravity
- Spatially covariant gravity: Perturbative analysis and field transformations
- Higher derivative scalar-tensor theory and spatially covariant gravity: the correspondence
- Covariant 3+1 correspondence of the spatially covariant gravity and the degeneracy conditions
- Quadratic DHOST theories revisited
Cited by in corpus (7)
- Gravitational wave constraints on Lorentz and parity violations in gravity: high-order spatial derivative cases
- Quasinormal modes and grey-body factors of regular black holes with a scalar hair from the Effective Field Theory
- Gravitational wave constraints on spatial covariant gravities
- Ultraviolet Unitarity Violations in Non-minimally Coupled Scalar-Starobinsky Inflation
- Spatially covariant gravity with nonmetricity
- Scalar fields with derivative coupling to curvature in the Palatini and the metric formulation
- Ghost Free Theory in Unitary Gauge: A New Candidate