F(U)-Gravity: A Unified Framework for Singularity Resolution, Dark Matter, and Quantum Gravity

I introduce F(U)-gravity, a modified gravitational framework extending Einstein’s theory by incorporating an energy-dependent curvature function F(U). This approach addresses fundamental issues in cosmology and quantum gravity, including singularity resolution, the nature of dark matter, and deviations from standard general relativity. By modifying the Einstein-Hilbert action, I derive new field equations and examine their thermodynamic and observational consequences. My theoretical predictions suggest distinct signatures in gravitational wave echoes and cosmic microwave background anomalies, which could provide experimental validation through upcoming LIGO and LISA observations. This work builds upon approaches such as those proposed by Rosen [Phys. Rev. 57, 147 (1940)] and Stelle [Phys. Rev. D 16, 953 (1977)], offering a novel perspective on the quantum nature of spacetime.