Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability

By D. Langlois, K. Noui. 2015

642 citations recorded by the source corpus.

Theories with higher order time derivatives generically suffer from ghost-like instabilities, known as Ostrogradski instabilities. This fate can be avoided by considering ``degenerate'' Lagrangians, whose kinetic matrix cannot be inverted, thus leading to constraints between canonical variables and a reduced number of physical degrees of freedom. In this work, we derive in a systematic way the degeneracy conditions for scalar-tensor theories that depend quadratically on second order derivatives of a scalar field. We thus obtain a classification of all degenerate theories within this class of scalar-tensor theories. The quartic Horndeski Lagrangian and its extension beyond Horndeski belong to these degenerate cases. We also identify new families of scalar-tensor theories with the property that they are degenerate despite the nondegeneracy of the purely scalar part of their Lagrangian.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0c652567791fbc91ddd5544ae961c4f567cdc103

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Citations in the corpus

Dark energy and modified gravity in degenerate higher-order scalar–tensor (DHOST) theories: A review (2018, methodology): “DHOST theories were constructed and fully classified up to quadratic order (in second-order derivatives) in [13] (see also [16–18]) and later up to cubic order in [15].”
Effective description of higher-order scalar-tensor theories (2017, methodology): “(5)More precisely, as explained in detail in [26], one first introduces an auxiliary variable that includes the time derivative of the scalar field φ̇, as well as the lapse and the shift, so that all second-order time derivatives φ̈ are absorbed by the velocity of this auxiliary variable and there a”
A systematic approach to generalisations of General Relativity and their cosmological implications (2018, methodology): “We can start with the most general Lagrangian up to cubic order in Πμν [160, 164, 162]”
Gravitational wave decay into dark energy (2018, background): “2˚ ;˚;˙˚; ;˙) F 5(˚;X)ˆ˙ 00ˆ0˙0˚ ;˚ ;0˚ ; 0˚ ;ˆˆ˚ ;˙˙0 ; (74) 15 and F 4 and F 5 are related by XG 5;XF 4 = 3F 5 [G 4 2XG 4;X (X=2)G 5;˚] ; (75) in order for the theory to be degenerate [43]. The relevant parameters in eq. (1) can be written in terms of the covariant functions G 4, G 5, F 4 and F 5 ”
Hamiltonian analysis of higher derivative scalar-tensor theories (2015, background): “This apparent paradox is resolved by the fact that some nondegenerate, and thus unhealthy, theories can appear degenerate in the unitary gauge, as discussed in [16].”
Stellar structure models in modified theories of gravity: Lessons and challenges (2019, background): “It includes as members the beyond Horndeski class [135, 136, 137] and the even more general class called degenerate higher-order scalar-tensor (DHOST) theories [134].”
Generalized Proca action for an Abelian vector field (2015, background): “[8–11]), thereby forming the vector Galileon case [12, 13], which was investigated thoroughly [14–21].”
Degenerate higher order scalar-tensor theories beyond Horndeski and disformal transformations (2016, methodology): “In this section, we summarize the main results obtained in [7], as well as some additional elements derived in [8], and present all the quadratic DHOST theories, i.”
Extended scalar-tensor theories of gravity (2016, methodology): “2 Non-minimally coupled theories In this section we include a non-minimal coupling term [7] LR[G] = G(φ, X)R .”
Scalar-tensor theories and modified gravity in the wake of GW170817 (2017, methodology): “All DHOST theories with a quadratic dependence on second derivatives were obtained in [3] by using this degeneracy condition.”
Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order (2016, methodology): “42), one recovers the quadratic theories identified in [19]; they are summarised in Appendix C.”
Cosmological tests of modified gravity (2015, background): “This generally gives rise to derivatives higher than second order, but it does not necessarily mean that an extra propagating degree of freedom is present [93, 94].”