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 analyzing 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 là Brans–Dicke. We identify the most general transformation preserving second-order field equations and discuss the issue of viable frames for this kind of theory, in particular, the possibility to cast the action in the so-called Einstein frame. Interestingly, we find that only for a subset of the Horndeski Lagrangian such a frame exists. Finally, we investigate the transformation properties of such frames under field redefinitions and frame transformations and their reciprocal relationship.

Disformal invariance of second order scalar-tensor theories: Framing the Horndeski action / Bettoni, D; Liberati, Stefano. - In: PHYSICAL REVIEW D, PARTICLES, FIELDS, GRAVITATION, AND COSMOLOGY. - ISSN 1550-7998. - 88:8(2013). [10.1103/PhysRevD.88.084020]

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

Liberati, Stefano
2013-01-01

Abstract

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 analyzing 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 là Brans–Dicke. We identify the most general transformation preserving second-order field equations and discuss the issue of viable frames for this kind of theory, in particular, the possibility to cast the action in the so-called Einstein frame. Interestingly, we find that only for a subset of the Horndeski Lagrangian such a frame exists. Finally, we investigate the transformation properties of such frames under field redefinitions and frame transformations and their reciprocal relationship.
2013
88
8
http://link.aps.org/doi/10.1103/PhysRevD.88.084020
https://arxiv.org/abs/1306.6724
Bettoni, D; Liberati, Stefano
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/11750
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