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

Abstract

We establish a correspondence between higher-derivative gravitational scalar-tensor theories of the form $Ψ(R,(\nabla R)^2,\Box R)$ 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.

Figures (2)

• Figure 1: Illustration of the correspondence between the $\Psi$ and $f$ formulations.
• Figure 2: Rescaled deviation $R_*^{\delta} G(\phi)$ with $\delta = 0.426$ for $R_* = 2$ (blue curve) and $R_* = 100$ (orange curve), and $\epsilon=10^{-3}$. The shaded region shows the range of $R_*^{\delta}G(\phi)$ as $R_*$ varies between $1$ and $100$. For $\phi \in [0,1]$, the magnitude is of order $10^{-1}$ in this domain.