A connection between Gravitational Scalar-Tensor theories and Generalized Hybrid theories

TL;DR

This paper establishes a formal link between higher-derivative scalar-tensor theories and generalized hybrid metric-Palatini models, enabling reformulation and reconstruction of these theories in the Einstein frame.

Contribution

It provides an explicit dictionary connecting the functions of higher-derivative theories to hybrid models, facilitating their analysis and comparison.

Findings

Both frameworks can be reformulated as Einstein gravity with two scalar fields.

An explicit dictionary relates the defining functions of the two theories.

The approach is illustrated with concrete examples.

Abstract

We establish a correspondence between higher-derivative gravitational scalar-tensor theories of the form $\Psi(R,(\nabla R)^2,\Box R)$ and generalized hybrid metric-Palatini models $f(R,\mathcal{R})$. Restricting to the physically relevant case of linear dependence on $\Box R$, we make explicit that both frameworks can be reformulated in the Einstein frame as General Relativity minimally coupled to two interacting scalar fields, thereby opening the possibility of finding theories that are dynamically equivalent. This correspondence provides an explicit dictionary relating the functions that define the higher-derivative theory to the hybrid function $f(R,\mathcal{R})$, allowing for reconstruction in both directions. We illustrate the usefulness of the procedure with explicit examples.