Do ghost fields really make massive gravity invalid?

TL;DR

This paper challenges the assumption that ghost fields necessarily invalidate massive gravity theories by presenting an example where ghost modes are controlled, maintaining positive energy and stability.

Contribution

It introduces a massive gravity theory with ghost fields that avoids instability through global configuration restrictions, countering previous assumptions.

Findings

Ghost modes can be stabilized with global constraints.

Energy remains positive despite the presence of ghost-like modes.

The theory remains consistent and stable under certain conditions.

Abstract

Theories which contain ghost fields are considered to be invalid. It is assumed that for such theories the energy is unbounded from below, and the theory will be unstable, allowing the creation of particle pairs with arbitrarily large positive and negative energies. Such ghost fields are a serious problem for theories of massive gravity. We present here an example of such a theory of gravity with a ghost field which avoids this problem. While its equations are locally equivalent to those of a theory of massive gravity with a ghost field, global restrictions of the configuration space have the result that the ghost mode has to remain small, and the energy has to remain positive. As a consequence, the existence of a ghost-like mode in the equations of the theory is not a decisive argument against this theory.