Exploring gravitational theories beyond Horndeski

@article{Gleyzes2014ExploringGT,
  title={Exploring gravitational theories beyond Horndeski},
  author={J'erome Gleyzes and David Langlois and Federico Piazza and Filippo Vernizzi},
  journal={Journal of Cosmology and Astroparticle Physics},
  year={2014},
  volume={2015},
  pages={018 - 018}
}
We have recently proposed a new class of gravitational scalar-tensor theories free from Ostrogradski instabilities, in ref. [1]. As they generalize Horndeski theories, or “generalized” galileons, we call them G3. These theories possess a simple formulation when the time hypersurfaces are chosen to coincide with the uniform scalar field hypersurfaces. We confirm that they contain only three propagating degrees of freedom by presenting the details of the Hamiltonian formulation. We examine the… 
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TLDR
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References

SHOWING 1-10 OF 57 REFERENCES
Unifying framework for scalar-tensor theories of gravity
A general framework for effective theories propagating two tensor and one scalar degrees of freedom is investigated. Geometrically, it describes dynamical foliation of spacelike hypersurfaces coupled
Hamiltonian structure of scalar-tensor theories beyond Horndeski
We study the nature of constraints and the Hamiltonian structure in a scalar-tensor theory of gravity recently proposed by Gleyzes, Langlois, Piazza and Vernizzi (GLPV). For the simple case with
A simplified approach to general scalar-tensor theories
The most general covariant action describing gravity coupled to a scalar field with only second order equations of motion, Horndeski's theory (also known as ``Generalized Galileons''), provides an
Effective theory for the Vainshtein mechanism from the Horndeski action
tarting from the general Horndeski action, we derive the most general effective theory for scalar perturbations around flat space that allows us to screen fifth forces via the Vainshtein mechanism.
Disformal invariance of second order scalar-tensor theories: Framing the Horndeski action
The Horndeski action is the most general one involving a metric and a scalar field that leads to second order field equations in four dimensions. Being the natural extension of the well known
From k-essence to generalised Galileons
We determine the most general scalar field theories which have an action that depends on derivatives of order two or less, and have equations of motion that stay second order and lower on flat
Models of non-relativistic quantum gravity: the good, the bad and the healthy
Hořava’s proposal for non-relativistic quantum gravity introduces a preferred time foliation of space-time which violates the local Lorentz invariance. The foliation is encoded in a dynamical scalar
Covariant Galileon
Abstract We consider the recently introduced “galileon” field in a dynamical spacetime. When the galileon is assumed to be minimally coupled to the metric, we underline that both field equations of
The Effective Field Theory of Inflation/Dark Energy and the Horndeski Theory
The effective field theory (EFT) of cosmological perturbations is a useful framework to deal with the low-energy degrees of freedom present for inflation and dark energy. We review the EFT for
Spatially covariant theories of a transverse, traceless graviton: Formalism
General relativity is a covariant theory of two transverse, traceless graviton degrees of freedom. According to a theorem of Hojman, Kuchar, and Teitelboim, modifications of general relativity must
...
...