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.
|Titolo:||Disformal invariance of second order scalar-tensor theories: Framing the Horndeski action|
|Autori:||Bettoni D; Liberati S|
|Rivista:||PHYSICAL REVIEW D, PARTICLES, FIELDS, GRAVITATION, AND COSMOLOGY|
|Data di pubblicazione:||2013|
|Digital Object Identifier (DOI):||10.1103/PhysRevD.88.084020|
|Appare nelle tipologie:||1.1 Journal article|