Gravitational scalar-tensor theory

Understand

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.