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

Dario Bettoni and Stefano Liberati
Phys. Rev. D 88, 084020 – Published 14 October 2013

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.

  • Received 12 July 2013

DOI:https://doi.org/10.1103/PhysRevD.88.084020

© 2013 American Physical Society

Authors & Affiliations

Dario Bettoni* and Stefano Liberati

  • SISSA/ISAS, Via Bonomea 265, 34136 Trieste, Italy
  • INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste, Italy

  • *bettoni@sissa.it
  • liberati@sissa.it

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Issue

Vol. 88, Iss. 8 — 15 October 2013

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