The Zero-Energy Universe Hypothesis: Integrating Relativistic Field and Curvature Energy in FLRW Cosmology

The Zero-Energy Universe hypothesis posits that the total energy content of the observable universe is identically zero, with all positive mass and kinetic energy exactly balanced by negative gravitational potential and spacetime curvature energy. While a standard Newtonian calculation for a uniform sphere bounded by the Hubble horizon accounts for classical gravitational binding energy, this classical potential magnitude offsets only thirty percent of the total rest-mass energy. In this paper, the author examines the formal cosmic mass and energy derivations within a flat Friedmann-Lemaître-Robertson-Walker universe and highlights the mathematical insufficiency of a purely Newtonian framework. The Relativistic Field and Curvature Contribution is introduced to account for the energy stored in expanding spacetime geometry, relativistic field dynamics, and global horizon effects in General Relativity. By incorporating this geometric field energy, which supplies the remaining seventy percent of negative energy, this paper demonstrates that the positive rest-mass energy, Newtonian potential energy, and relativistic curvature contribution sum precisely to zero, offering a complete and consistent energy balance for the zero-energy cosmological model.