Removing Ostrogradski ghost from degenerate gravity theories

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.

20 pages, LaTex, slight modification in texts, to appear in PRD

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• Ostrogradsky-Hamilton approach to geodetic brane gravity
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• Removal of instabilities of the higher derivative theories in the light of antilinearity
• Treating Ostrogradski instability for Gallilean invariant Chern Simon's model via \mathcal{PT} symmetry
• Sub-Planckian scale and limits for $f(R)$ models
• Ghosts in higher derivative Maxwell-Chern-Simon's theory and $\mathcal{P}\mathcal{T}-$symmetry