Abstract: Quadratic gravity offers a compelling path to a renormalizable quantum theory of gravitational interactions. However, renormalizability comes at the price of unitarity, which is violated by the presence of ghost particles, undermining its physical viability. Purely virtual particles (PVP) provide a sharp resolution to this problem. They are novel degrees of freedom that can mediate interactions without ever appearing as on-shell states, allowing quadratic gravity to preserve its ultraviolet consistency while restoring unitarity. 
In this talk, I will briefly review the ultraviolet behavior of Einstein gravity and the relation between renormalizability and unitarity violation in quadratic gravity. I will then show how PVP can be consistently incorporated into quantum field theory and show the resulting unitary version of quadratic gravity. Finally, I will outline its predictions in inflationary cosmology and close with a short outlook on possible applications of PVP in particle physics.