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Purely virtual particles, or fakeons, are degrees of freedom of a new type that mediate interactions but cannot appear as external on-shell states. The main application of fakeons is quantum gravity, which can be made both renormalizable and unitary. After discussing in detail how to endow quantum field theory with fakeons, I will present the main features of the theory of quantum gravity and show its predictions in inflationary cosmology. Finally, I will conclude with some remarks on fakeons in the context of particle physics.