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

TL;DR

This paper demonstrates that a broad class of scalar-tensor theories, characterized by a general Lagrangian, are free from the Ostrogradsky ghost, ensuring their classical stability and limiting their degrees of freedom.

Contribution

It provides a Hamiltonian analysis proving the absence of Ostrogradsky ghosts in a wide class of scalar-tensor theories with complex Lagrangians.

Findings

Theories are free from Ostrogradsky ghost.

These theories have at most 3 classical degrees of freedom.

The analysis applies to Lagrangians with various geometric and scalar quantities.

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.