Quantum Gravity Effects in Primordial Black Holes: A Rigorous Framework for Memory Burden Phenomenology and Multi-Messenger Constraints

We develop a comprehensive theoretical framework for primordial black hole (PBH) evolution incorporating quantum gravity effects through the memory burden mechanism. Our approach addresses fundamental limitations in previous treatments through: (1) microscopic derivation of memory burden parameters from quantum information theory, (2) systematic uncertainty quantification with conservative observational predictions, (3) comprehensive validation against known astrophysical constraints, and (4) robust statistical analysis using Bayesian model comparison. The memory burden effect, arising from quantum microstate saturation, provides exponential suppression of Hawking evaporation when black holes emit N ∼ Sinitial particles. We derive the critical mass scale Mc = (ℏc/G)1/2 expp Sinitial/(4π) ∼ 107−9 g from first principles, with theoretical uncertainties spanning one order of magnitude. Using conservative statistical analysis and systematic error propagation, we find that memory-burdened PBHs can constitute up to fPBH ≤ 0.1 of dark matter in the mass range 106–109 g without violating current observational constraints. Our framework predicts: (i) 5–25 excess neutrino events per year in IceCube-Gen2 for realistic PBH abundances, (ii) enhanced stochastic gravitational wave backgrounds detectable by LISA with > 2σ significance, and (iii) distinctive gamma-ray spectral features observable in next-generation air Cherenkov telescopes. This work establishes a robust foundation for testing quantum gravity theories through precision multi-messenger astrophysics while maintaining rigorous theoretical grounding and conservative observational predictions. We provide a complete open-source implementation enabling collaborative research and reproducible science.