Do ghost fields really make massive gravity invalid?

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.