Cosmological Evolution of Primordial Black Holes: UV/IR Decoupling and the KM3NeT 220 PeV Neutrino Anomaly

The recent observation of a 220 PeV neutrino event (KM3-230213A) by the KM3NeT observatory presents a formidable challenge to standard astrophysical source models. We investigate the hypothesis that this ultra-high-energy signature originates from the terminal evaporation burst of a Primordial Black Hole (PBH). Since PBH evolution spans cosmic history, static vacuum approximations fail to capture early-universe dynamics. Embedding the PBH in a cosmological background via the McVittie spacetime, we demonstrate that early-universe cosmological accretion and expansion-suppressed Hawking emission shift the required initial mass window for a terminal burst occurring today. We show that although the early universe environment dictates the black hole's overall lifespan, its final explosion today (z about 0) is governed by standard Schwarzschild thermodynamics. This mechanism naturally produces the intense 220 PeV local flux while suppressing early emissions, thereby satisfying diffuse isotropic background limits. Consequently, this dynamical framework alters the mapping between current ultra-high-energy neutrino observables and the primordial curvature perturbations that seeded them.