When is Multimetric Gravity Ghost-free?

TL;DR

This paper analyzes the presence of ghosts in multimetric gravity models using Hamiltonian methods, revealing conditions under which these models are ghost-free or contain ghosts, especially in trimetric and loop interaction cases.

Contribution

It introduces a Hamiltonian constraint analysis approach to determine ghost-freedom in multimetric gravity, clarifying when ghosts appear or are eliminated in various models.

Findings

Trimetric gravity generally contains a ghost.

Removing one interaction makes trimetric gravity ghost-free.

Loop interactions in multimetric gravity always contain ghosts.

Abstract

We study ghosts in multimetric gravity by combining the mini-superspace and the Hamiltonian constraint analysis. We first revisit bimetric gravity and explain why it is ghost-free. Then, we apply our method to trimetric gravity and clarify when the model contains a ghost. More precisely, we prove trimetric gravity generically contains a ghost. However, if we cut the interaction of a pair of metrics, trimetric gravity becomes ghost-free. We further extend the Hamiltonian analysis to general multimetric gravity and calculate the number of ghosts in various models. Thus, we find multimetric gravity with loop type interactions never becomes ghost-free.