Gravitational scalar-tensor theory

TL;DR

This paper introduces a new class of gravity theories involving Ricci scalar derivatives, which are free from ghosts and have specific degrees of freedom, expanding the landscape of modified gravity models.

Contribution

The authors classify and analyze a novel family of higher-derivative gravity theories with specific Lagrangian forms, establishing their ghost-free nature and equivalence to generalized bi-Galileon theories.

Findings

Theories are free from ghosts with appropriate Lagrangian choices.

The models have 2 scalar and 2 tensor degrees of freedom.

Established equivalence to generalized bi-Galileon theories.

Abstract

We consider a new form of theories of gravity in which the action is written in terms of the Ricci scalar and its first and second derivatives. Despite the higher derivative nature of the action, the theory is free from ghost under an appropriate choice of the functional form of the Lagrangian. This model possesses $2+2$ physical degrees of freedom, namely $2$ scalar degrees and $2$ tensor degrees. We exhaust all such theories with the Lagrangian of the form $f(R, (\nabla R)^2, \Box R)$, where $R$ is the Ricci scalar, and then show some examples beyond this ansatz. In course of analysis, we prove the equivalence between these examples and generalized bi-Galileon theories.