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

TL;DR

This paper explores how disformal transformations preserve the second order nature of Horndeski theories, analyzing frame choices and their physical equivalence, extending the understanding of scalar-tensor theories.

Contribution

It identifies the most general disformal transformations that preserve second order equations in Horndeski theories and discusses frame viability and physical equivalence.

Findings

Disformal transformations preserve second order field equations in Horndeski theories.

The paper discusses the Einstein frame and its physical relevance.

It establishes conditions for frame equivalence in scalar-tensor theories.

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 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.