Unifying framework for scalar-tensor theories of gravity

By Xian Gao. 2014

164 citations recorded by the source corpus.

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 to a general background, in which the scalar mode encodes the fluctuation of the hypersurfaces. Within this framework, various models in the literature---including $k$-essence, Horndeski theory, the effective field theory of inflation, ghost condensate as well as the Ho\v{r}ava gravity---get unified. Our framework generalizes the Horndeski theory in the sense that, it propagates the correct number of degrees of freedom, although the equations of motion are generally higher order. We also identify new operators beyond the Horndeski theory, which yield second order equations of motion for linear perturbations around an a Friedmann-Robertson-Walker background.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/fcf55ed301bfa9278ca21ba0c28eb7e146e7fd37

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Citations in the corpus

Generic instabilities of nonsingular cosmologies in Horndeski theory: A no-go theorem (2016, background): “The resultant gradient instability is cured by the introduction of higher order spatial derivatives arising in the effective field theory approach [29] or in theories beyond Horndeski [30, 40, 41].”
Hamiltonian analysis of higher derivative scalar-tensor theories (2015, methodology): “In the context of higher order scalar-tensor theories, the idea that second-order EulerLagrange equations are necessary to avoid ghost-like instabilities was questioned in [11], by exhibiting a theory obtained from Einstein-Hilbert via disformal transformation, and in [12], by proposing two extensio”
Dark energy and modified gravity in degenerate higher-order scalar–tensor (DHOST) theories: A review (2018, background): “Another possibility to obtain healthy scalartensor theories with higher derivatives is to give up general covariance and work directly with spatially covariant theories [28, 29].”
Extended scalar-tensor theories of gravity (2016, methodology): “We derive the conditions for the existence of a primary constraint that prevents the propagation of an additional dangerous mode associated with higher order equations of motion.”
Horndeski theory and beyond: a review (2019, background): “[49, 50, 51, 52, 53] for a further generalization of the ADM description of scalar-tensor theories.”
Exploring gravitational theories beyond Horndeski (2014, unknown): “In analogy with Horava’s gravity, one could consider various combinations of the intrinsic curvature tensor and its spatial derivatives, as well as various combinations of the extrinsic curvature tensor, as recently discussed in [30].”
Degenerate higher order scalar-tensor theories beyond Horndeski and disformal transformations (2016, background): “[13–17], and [18] for scalar tensor theories that explicitly break spacetime covariance [19].”
The Effective Field Theory of nonsingular cosmology (2016, background): “It offers a unifying platform to deal with the cosmological perturbations of all kinds of theories, such as the Horndeski theory and its beyond, the Horava gravity [43], and the spatial covariant gravity [44, 45].”
A unifying description of dark energy (2014, methodology): “However, it has been shown in [19, 20] (see also [24] for similar analysis and conclusion and [21, 22, 25] for extensions) that an action composed of the Lagrangians L2 ≡ A2(t,N) , L3 ≡ A3(t,N)K , L4 ≡ A4(t,N) ( K(2) −KijK )”
hi_class: Horndeski in the Cosmic Linear Anisotropy Solving System (2016, background): “The models can be extended even further to those which contain higher derivatives in space but not in time [44–47].”