The Spin-2 Ghost as an Intrinsic Ultraviolet Regulator in Quadratic Gravity

We investigate the ultraviolet (UV) behavior of four-derivative quadratic gravity in fourdimensions, retaining the massive spin-2 ghost as a dynamical ingredient rather than eliminatingit. At the linearized level the graviton propagator splits into a massless spin-2 poleand a massive spin-2 pole with negative residue, so that the combined propagator fallsas k−4 at large momentum and loop integrals become power-counting renormalizable. Thisbuilt-in Pauli–Villars-like softening is the mechanism underlying Stelle’s renormalizability ofquadratic gravity, and we treat it as established rather than novel: the ghost pole is the subtractor.Our contribution is a synthesis. We argue that this same retained, negative-energyspin-2 mode—the object responsible for the UV subtraction—is realized cosmologically asthe intrinsic shear of an anisotropic vacuum solution and drives a non-singular bounce,so that the ultraviolet-regulator role and the cosmological-bounce role are carried by onemode. We revisit the loop structure and the conditions for an effectively UV-complete interpretation,and we address unitarity not by rendering the ghost purely virtual but bydistinguishing its status as an asymptotic scattering state (constrained) from its status asan on-shell classical background (physical and load-bearing). We compare the mechanismto Agravity, asymptotic safety, nonlocal gravity, and fakeon formulations, and to the closestcosmological precedent—the light-Weyl-ghost model of Ivanov and Tokareva—from whichour scenario differs by the opposite (negative) energy-sign choice and the opposite cosmologicalfate. The massive spin-2 ghost is a feature enabling UV softness, not a flaw to beremoved.Provenance. This version was generated by an AI system (Claude, Anthropic) under humandirection, with all symbolic results machine-verified; see the Acknowledgements for theattribution model and multi-model lineage.