Resolving the Ostrogradsky Ghost Problem for a Class of Scalar-tensor Theories

Abstract

We perform a Hamiltonian analysis and prove that a large class of scalar-tensor theories whose Lagrangian is given by a generic function $F\left(K_{ab},N,R_{ab},h^{ab},\nabla_a,t\right)$ is free from the Ostrogradsky ghost, and thus these theories contain at most 3 degrees of freedom at classical level.

4 pages, no figure; V2, remarks added, minor errors corrected, English improved; V3, typos corrected, more remarks added; V4, typos corrected, more remarks and references added, notations improved, Letter format