Transforming gravity: from derivative couplings to matter to second-order scalar-tensor theories beyond the Horndeski Lagrangian

By Miguel Zumalac'arregui, Juan Garc'ia-Bellido Madrid Ift, U. Heidelberg, Itp. 2013

479 citations recorded by the source corpus.

We study the structure of scalar-tensor theories of gravity based on derivative couplings between the scalar and the matter degrees of freedom introduced through an effective metric. Such interactions are classified by their tensor structure into conformal (scalar), disformal (vector), and extended disformal (traceless tensor), as well as by the derivative order of the scalar field. Relations limited to first derivatives of the field ensure second-order equations of motion in the Einstein frame and hence the absence of Ostrogradski ghost degrees of freedom. The existence of a mapping to the Jordan frame is not trivial in the general case, and can be addressed using the Jacobian of the frame transformation through its eigenvalues and eigentensors. These objects also appear in the study of different aspects of such theories, including the metric and field redefinition transformation of the path integral in the quantum mechanical description. Although second-order in the Einstein frame, generic disformally coupled theories are described by higher-order equations of motion in the Jordan frame. This apparent contradiction is solved by the use of a hidden constraint: the contraction of the metric equations with a Jacobian eigentensor provides a constraint relation for the higher field derivatives, which allows one to express the dynamical equations in a second-order form. This signals a loophole in Horndeski’s theorem and allows one to enlarge the set of scalar-tensor theories which are Ostrogradski stable. The transformed Gauss-Bonnet terms are also discussed for the simplest conformal and disformal relations.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/0848132a97631e50f6301045630205319bb7ec64

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Citations in the corpus

Healthy degenerate theories with higher derivatives (2016, background): “Recently it has been pointed out that one can find healthy extensions of Horndeski theories [7, 8], whose Euler-Lagrange equations involve higher order derivatives (see also [9] for an earlier example of theory “beyond Horndeski”).”
A systematic approach to generalisations of General Relativity and their cosmological implications (2018, background): “However, as initiated in [58, 59] this restriction is not necessary.”
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”
Scalar-tensor theories and modified gravity in the wake of GW170817 (2017, methodology): “Another subclass of DHOST theories was found earlier in [8], via disformal transformations of the Einstein-Hilbert action.”
Exploring gravitational theories beyond Horndeski (2014, background): “Other fissures in the standard lore concerning Horndeski theories were pointed out in [18], which studied scalar-tensor theories generated by disformal relations [19] g̃μν = Ω (2)(X,φ)gμν + Γ(X,φ)∂μφ∂νφ , (2) where X ≡ g∂μφ∂νφ.”
Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability (2015, background): “Recently it was realized that requiring second order equations of motion is in fact not mandatory and extensions of Horndeski’s quartic and quintic Lagrangians were proposed in [14, 15] (an earlier example of theory beyond Horndeski was constructed in [16] via the use of disformal transformations).”
Dark energy and modified gravity in degenerate higher-order scalar–tensor (DHOST) theories: A review (2018, background): “A first breach in this argument was provided in [8], where it was noticed that (invertible) field redefinitions of the metric of the form [9]”
Horndeski theory and beyond: a review (2019, methodology): “The first example of degenerate higher-order scalar-tensor (DHOST) theories beyond Horndeski [159] was obtained by performing a disformal transformation [160]”
Extended scalar-tensor theories of gravity (2016, background): “They study degeneracy conditions for the kinetic matrix associated with Lagrangians that are at most quadratic in the scalar second derivatives.”
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].”
Cosmological tests of modified gravity (2015, background): “(38), the equations of motion can be written in the second order form despite the appearance of the higher derivative terms due to a hidden constraint [82] (see also [83, 84]).”