Higher derivative gravity with spontaneous symmetry breaking: Hamiltonian analysis of new covariant renormalizable gravity

TL;DR

This paper performs a Hamiltonian analysis of a covariant renormalizable gravity theory with higher derivatives and spontaneous symmetry breaking, revealing the presence of a ghost degree of freedom that destabilizes the theory.

Contribution

It provides a Hamiltonian formulation of the new covariant renormalizable gravity and identifies additional degrees of freedom, including a destabilizing ghost, challenging previous claims.

Findings

CRG contains two extra degrees of freedom.

One degree of freedom is a ghost with negative energy.

The ghost destabilizes the theory due to its interactions.

Abstract

In order to explore some general features of modified theories of gravity which involve higher derivatives and spontaneous Lorentz and/or diffeomorphism symmetry breaking, we study the recently proposed new version of covariant renormalizable gravity (CRG). CRG attains power-counting renormalizability via higher derivatives and introduction of a constrained scalar field and spontaneous symmetry breaking. We obtain an Arnowitt-Deser-Misner representation of the CRG action in four-dimensional spacetime with respect to a foliation of spacetime adapted to the constrained scalar field. The resulting action is analyzed by using Hamiltonian formalism. We discover that CRG contains two extra degrees of freedom. One of them carries negative energy (a ghost) and it will destabilize the theory due to its interactions. This result is in contrast with the original paper [Phys. Lett. B 701, 117 (2011), arXiv:1104.4286 [hep-th]], where it was concluded that the theory is free of ghosts and renormalizable when we analyze fluctuations on the flat background.