Renormalization Group Analysis of Singularity Avoidance in Loop Quantum Cosmology

Loop Quantum Cosmology (LQC) resolves cosmological singularities through quantum geometric effects. We perform a Renormalization Group (RG) analysis of the effective Friedmann equations derived by Ashtekar & Singh, introducing scale-dependent RG flows of gravitational constant G, critical density ρcrit, and matter density ρ. The resulting RG flow quantitatively shows how singularity avoidance occurs naturally within LQC, suggesting a crossover interpretation of the "big bounce". This RG perspective provides new insights into the scale-dependent nature of quantum gravitational effects.