Modified Field Equation With Gauss-Bonnet Gravity

This work provides a comprehensive analysis of modifications to the Einstein-Hilbert action, with a particular focus on Gauss-Bonnet (GB) gravity, and addresses the theoretical challenges in unifying quantum gravity frameworks with the GB gravitational modifications. By developing a novel fourth-order tensor methodology to manage derivative couplings, we establish a stable framework that eliminates higher-order derivative instabilities while enabling modified gravitational phenomena. The model maintains consistency with low-energy string theory constraints and generates testable predictions for black hole thermodynamics and cosmic expansion dynamics. Our results reconcile discrepancies between modified gravity theories and quantum field theory requirements, providing new mathematical tools for analyzing high-energy gravitational interactions. This work bridges critical gaps between theoretical formulations and observational evidence in cosmology, offering a unified approach to modeling gravitational interactions across quantum and cosmological scales.