# Removing Ostrogradski ghost from degenerate gravity theories

## TL;DR

This paper presents a method to eliminate Ostrogradski ghosts in higher derivative gravity theories by using Dirac's constraint analysis to make the Hamiltonian bounded from below, demonstrated on a Gauss-Bonnet gravity model.

## Contribution

It introduces a systematic approach to remove ghost-inducing constraints in degenerate higher derivative theories, ensuring a stable Hamiltonian.

## Key findings

- Successfully constructed a ghost-free Hamiltonian for Gauss-Bonnet gravity.
- Demonstrated the reduction of phase space dimension to eliminate ghost modes.
- Provided a general prescription applicable to constrained higher derivative systems.

## Abstract

The Ostrogradski ghost problem that appears in higher derivative system is considered for systems with constraints. A prescription for removal of the ghost creating momenta is described based on the Dirac's constraint analysis. It is shown how one can make the canonical Hamiltonian bounded from below by systematically removing the constraints appearing in the system thereby reducing the effective dimension of the phase space. To show the effect of higher derivative terms we consider the singularity free Gauss-Bonnet theory coupled via a matter field to the Einstein Hilbert action. Finally we construct the ghost free canonical Hamiltonian for the theory that is bounded from below.