Allowing gravitons to have 4 derivatives gives a renormalizable quantum theory of gravity, but at the price of introducing a spin 2 state with negative classical kinetic energy, called ghost. I will discuss different attempts to make sense of this theory, either accepting negative energy, or quantising as positive energy at the price of introducing negative norm. No final answer is provided, as open issues remain.

With support from FCT through project UIDB/00777/2020

© CFTP 2021