Disformal invariance of second order scalar-tensor theories: Framing the Horndeski action

By D. Bettoni, Stefano Liberati. 2013

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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 Scalar-Tensor theories, its structure and properties are worth analysing along the experience accumulated in the latter context. Here we argue that disformal transformations play, for the Horndeski theory, a similar role to that of conformal transformations for Scalar-Tensor theories a l`a Brans-Dicke. We identify the most general transformation preserving second order field equations and discuss the issue of viable frames for this kind of theories, in particular the possibility to cast the action in the so called Einstein frame. Finally, we investigate the physical equivalence of such frames and their reciprocal relationship.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/4b418668b17f1a1afdaeb7caaec6208047958763

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Citations in the corpus

Dark Energy in Light of Multi-Messenger Gravitational-Wave Astronomy (2018, background): “Just as Brans-Dicke is invariant under rescalings of the metric, Horndeski theories are invariant under field-dependent disformal transformations gμν → ḡμν = C(φ)gμν + D(φ)φ,μφ,ν , which amount to a redefinition of the Horndeski functions Gi (and the introduction of an explicit coupling to matter) (”
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.”
Horndeski theory and beyond: a review (2019, background): “rms in (110),¶ one ﬁnds that the degeneracy conditions are k If both C and D depend only on φ, the transformed ﬁeld equations remain of second order and so the Horndeski theory is mapped to Horndeski [161]. ¶ We require the degeneracy in any coordinate systems. It is argued in [170] that one can rel”
Dark energy and modified gravity in degenerate higher-order scalar–tensor (DHOST) theories: A review (2018, unknown): “with C = C(φ) and D = D(φ), as shown in [30].”
Disformal transformations, veiled General Relativity and Mimetic Gravity (2014, background): “The invariance, under such transformations, of field equations such as the Klein-Gordon, the Maxwell or the Horndeski equations of motion has recently been studied in, respectively, [3], [4], [5] - [6] and references therein.”
Exploring gravitational theories beyond Horndeski (2014, methodology): “This is analogous to the role played by disformal transformations with Γ = Γ(φ) for Horndeski theories, which leave them invariant [40].”
Effective description of higher-order scalar-tensor theories (2017, background): “Indeed, the structure of the action restricted to αH = αL = βA = 0 is invariant under this subset of transformations [60, 61].”
A unifying description of dark energy (2014, background): “(87) As shown in [39], Horneski theories are invariant under a restricted class of disformal transformations where Ω and Γ depend on φ only, not on X.”
Galileon gravity in light of ISW, CMB, BAO and H0 data (2017, background): “grangian is constructed out of g and matter m elds with no explicit occurrence of ˚. This is dierent from other models which often feature a coupling to the matter energy-momentum tensor (see e.g. [60,61] for the explicit Lagrangian). { 6 { Below, we focus specically on the model of Eq. (3.1). Howev”
Degenerate higher order scalar-tensor theories beyond Horndeski and disformal transformations (2016, background): “It was shown, in [11], that Horndeski theories transform into themselves under special disformal transformations where A and B depend on φ only, not on X.”