Quantum-Corrected Schwarzschild Metric and Its Implications for Black Hole Physics and Cosmology

We present a quantum-corrected Schwarzschild metric that extends General Relativity (GR) into the quantum regime, preserving its macroscopic successes while naturally resolving several longstanding problems in black hole physics and cosmology. By deriving the correction independently from both Quantum Field Theory (QFT) in curved spacetime and Loop Quantum Gravity (LQG), we establish that an additional term proportional to L_p^2 / r^2 modifies the Schwarzschild solution at small scales. This correction removes singularities, maintains quantum coherence at the event horizon, and introduces a second horizon structure, providing a possible resolution to the black hole information paradox.

Furthermore, we demonstrate that this quantum correction modifies the Friedmann equations, resulting in a natural mechanism for cosmic acceleration without requiring dark energy. This directly addresses the Hubble Tension by predicting an expansion rate of approximately 70.8 ± 0.6 km/s/Mpc, aligning early- and late-universe measurements. Additionally, the correction explains weak lensing anomalies observed in KiDS/DES surveys and allows for stable ultra-massive neutron stars beyond the Tolman-Oppenheimer-Volkoff (TOV) limit.

Our framework makes several falsifiable predictions that can be tested in upcoming observations, including gravitational wave echoes from quantum-corrected black holes (LIGO A+, LISA), neutron star mass distributions (NICER, LIGO), and CMB polarization anomalies (CMB-S4, LiteBIRD). If confirmed, this work represents a paradigm shift in quantum gravity and astrophysics, bridging the gap between microscopic quantum effects and large-scale cosmological evolution.