Degenerate higher order scalar-tensor theories beyond Horndeski and disformal transformations

By J. B. Achour, D. Langlois, K. Noui. 2016

298 citations recorded by the source corpus.

We consider all degenerate scalar-tensor theories that depend quadratically on second-order derivatives of a scalar field, which we have identified in a previous work. These theories, whose degeneracy, in general, ensures the absence of Ostrogradsky’s instability, include the quartic Horndeski Lagrangian and its quartic extension beyond Horndeski, as well as other Lagrangians. We study how all these theories transform under general disformal transformations and find that they can be separated into three main classes that are stable under these transformations. This leads to a complete classification modulo disformal transformations. Finally, we show that these higher order theories include mimetic gravity and some particular khronometric theories. They also contain theories that do not correspond, to our knowledge, to already studied theories, even up to disformal transformations.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Oceanography

View Paper: https://www.semanticscholar.org/paper/7a91c5330322072bdd70faf61036364b7598d556

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Citations in the corpus

Gravitational wave decay into dark energy (2018, background): “] or Extended Scalar-Tensor [44] theories. These theories can be obtained starting from beyond Horndeski and performing an invertible conformal transformation that depends on X, i.e. g !C(˚;X)g [45,44,46] (we assume Cis not linear in Xso that the transformation is invertible). Since this does not ”
Dark energy and modified gravity in degenerate higher-order scalar–tensor (DHOST) theories: A review (2018, methodology): “the relations between the new and old Lagrangians have been obtained explicitly in [16], with in particular”
Effective description of higher-order scalar-tensor theories (2017, methodology): “Using the terminology of [29] and [33], all the subclasses of DHOST theories are summarized in Table 1.”
Horndeski theory and beyond: a review (2019, methodology): “have a healthy degenerate theory [174]. A notable property of DHOST theories in class Ia is that all the Lagrangians can be mapped into a Horndeski Lagrangian through a disformal transformation (108) [167]. In other words, one can remove two of the three functions of φand Xin the quadratic DHOST sec”
Scalar-tensor theories and modified gravity in the wake of GW170817 (2017, background): “As shown in [33, 34], the quadratic DHOST theories of class I, thus including (8), can be reformulated as Horndeski theories via a disformal transformation of the metric, of the form g̃μν =C(X ,φ)gμν +D(X ,φ)φμ φν , but at the price of introducing a disformal coupling of matter to the metric.”
Mimetic Gravity: A Review of Recent Developments and Applications to Cosmology and Astrophysics (2016, background): “Another recent work confirmed in all generality that the original mimetic gravity theory suffers from ghost instability [140], in the following way.”
Hamiltonian analysis of higher derivative scalar-tensor theories (2015, background): “A discussion of this special case can be found in [39] (see also [40], where the first Hamiltonian analysis of mimetic gravity was presented).”
A systematic approach to generalisations of General Relativity and their cosmological implications (2018, methodology): “The classification is shown in figure 12 taken from [164].”
Testing modified gravity at cosmological distances with LISA standard sirens (2019, methodology): “Exploiting this property, Degenerate Higher Order Scalar-Tensor (DHOST) theories (see [85] for a recent review) have been constructed [86–88] and they represent (so far) the most general scalar-tensor theories that propagate a single scalar degree of freedom in addition to the helicity-2 mode of a m”