On the Ghost Problem of Conformal Gravity

TL;DR

This paper investigates the ghost problem in conformal gravity by analyzing metric perturbations around de Sitter and Minkowski backgrounds, revealing boundary conditions that can eliminate ghosts and align conformal gravity with Einstein gravity.

Contribution

It identifies boundary conditions that remove ghosts in conformal gravity and establishes conditions under which it matches Einstein gravity perturbations.

Findings

Ghosts are confirmed in conformal gravity on de Sitter and Minkowski backgrounds.

Certain boundary conditions can eliminate ghosts and align conformal gravity with Einstein gravity.

The study clarifies the role of boundary conditions in the consistency of conformal gravity.

Abstract

We study the metric perturbations around the de Sitter and Minkowski backgrounds in Conformal Gravity. We confirm the presence of ghosts in both cases. In the de Sitter case, by applying the Maldacena boundary conditions - the Neumann boundary condition and the positive-frequency mode condition - to the metric, we show that one cannot recover a general solution for the perturbations. In turn, alongside the Neumann boundary condition, we derive an additional condition with which the perturbations of conformal gravity and dS perturbations of Einstein gravity with cosmological constant coincide. We further show that the Neumann boundary condition does not lead to a general solution in Minkowski space. Conversely, we derive the alternative boundary conditions, with which we attain an agreement between the perturbations of conformal and Einstein gravity in full generality, thus removing the ghost of conformal gravity.