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We review the concept of purely virtual particle and its uses in quantumgravity, primordial cosmology and collider physics. The fake particle, or"fakeon", which mediates interactions without appearing among the incoming andoutgoing states, can be introduced by means of a new diagrammatics. Therenormalization coincides with the one of the parent Euclidean diagrammatics,while unitarity follows from spectral optical identities, which can be derivedby means of algebraic operations. The classical limit of a theory of physicalparticles and fakeons is described by an ordinary Lagrangian plus Hermitian,micro acausal and micro nonlocal self-interactions. Quantum gravity propagatesthe graviton, a massive scalar field (the inflaton) and a massive spin-2fakeon, and leads to a constrained primordial cosmology, which predicts thetensor-to-scalar ratio $r$ in the window $0.4\lesssim 1000r\lesssim 3.5$. Theinterpretation of inflation as a cosmic RG flow allows us to calculate theperturbation spectra to high orders in the presence of the Weyl squared term.In models of new physics beyond the standard model, fakeons evade variousphenomenological bounds, because they are less constrained than normalparticles. The resummation of self-energies reveals that it is impossible toget too close to the fakeon peak. The related peak uncertainty, equal to thefakeon width divided by 2, is expected to be observable.

Purely Virtual Particles in Quantum Gravity, Inflationary Cosmology and Collider Physics