Every child knows: there is nothing more dangerous than ghosts! Since children never lie, we also have to be extremely careful with theories that predict ghosts. While they are often assumed to be haunting spectres made of bed sheets that float over the floor, ghosts in theories of modified gravity should better be seen as some scalar fields that carry negative kinetic energy. If an apple would interact with such a field, then it could gain an arbitrary amount of energy from this ghostly field. In this case, the apple could jump up from the ground into the treetop! Let’s make it even worse: Imagine an empty box, nothing but vacuum. If there is a ghost then it can decay to arbitrary negative energies. But energy is still conserved, the positive amount of energy must go somewhere. And indeed, this energy will be used to create particles. Dramatically, this will happen instantaneously!
What will you see if you empty a box, close it and open it again? Exactly, it will still be empty and will not be filled with water or even 100 Euro bills. Moreover, nobody has seen any apple jumping up from the ground onto a branch of a tree.
Ghosts seem to be scary, too scary to accept them in any theory of gravity. But in a recent project, we really wanted to explore the limits and find out whether there is any way to live with them, without contradicting any observation. As a toy model, we have invented a new theory in which the graviton, the particle that mediates the gravitational force, is massive and comes along with a ghost. Since no theory of gravity can be valid on all energy scales, we assumed that for tiny scales physics does not necessarily behave identical for two different observers. Such a behaviour is indeed predicted by more fundamental theories like quantum gravity. In doing this, we killed two birds with one stone: We have shown that the ghost in our theory is tame and will not lead to disastrous predictions like an instantaneous decay of the vacuum or balls rolling up a hill spontaneously. Furthermore, we present the first consistent model of a massive graviton that is cosmologically viable and does not need an additional graviton, that is assumed to exist in extensions like bimetric gravity or even trigravity.