Memory-Burden Suppression of Hawking Radiation and Neutrino Constraints on Primordial Black Holes

Abstract: We investigate the impact of quantum gravitational memory-burden effects on high-energy neutrino signals from evaporating primordial black holes and the resulting constraints from IceCube observations. Treating the backreaction as an energy-dependent deformation of the Hawking emission spectrum, we show that the high-energy tail is suppressed while the infrared behaviour remains unchanged. We derive analytically that this modification reduces the total luminosity and extends the evaporation lifetime by a mass-independent factor determined solely by the suppression parameter. Using an effective treatment of cosmological redshift, we compute the diffuse neutrino flux from a primordial black hole population and compare it with the observed astrophysical neutrino spectrum to constrain the primordial black hole dark matter fraction. We find that the suppression onset lies within the IceCube sensitivity window, leading to a direct reduction of the observable signal and a systematic weakening of the inferred bounds. Our results provide a controlled phenomenological framework for assessing the impact of quantum gravitational corrections on neutrino probes of primordial black hole evaporation.