Disformal invariance of second order scalar-tensor theories

TL;DR

This paper demonstrates that disformal transformations preserve the structure of Horndeski's second-order scalar-tensor theories, similar to how conformal transformations relate to Brans-Dicke theories, highlighting a key invariance property.

Contribution

It establishes the invariance of Horndeski theories under disformal transformations, extending the understanding of their structural properties and symmetries.

Findings

Disformal transformations leave the form of Horndeski action invariant.

Disformal invariance generalizes the role of conformal invariance in scalar-tensor theories.

Provides insights into the symmetry structure of second-order 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 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 la Brans-Dicke.