• Metastability of negative kinetic energy

A renormalizable quantum field theory of gravity is possible when considering higher derivative theories. These kind of theories have problems with unitarity. Loosing the unitarity property, the theories admit negative kinetic energy states. When a positive-energy degree of freedom interacts with a negative-energy degree of freedom ("ghost"), runaways can take place i.e energy's explosion. The goal of this work is to find if metastable states can exist considering negative kinetic energy in classical mechanics and classical field theory. The time of stability is computed, varying the value of the coupling. Positive-energy degree of freedom and negative ones interact by means of a quartic interaction. Summarising the results, in classical mechanics ghost are stable if the couplings are "small". In classical field theory the number of resonances is infinite, therefore runaways are almost certain. A statistical analysis is performed and it is shown that the rate of energy's explosion is slow if compared with cosmological time scales.