Emergent Geometry, Quantization, and Cosmological Dynamics from a Single Nonlinear Field

This work presents a unified theoretical framework based on the existence of a single fundamental scalar field, denoted ψ, which represents the effective geometric curvature of the underlying physical substrate. All observed physical phenomena — including particle structure, quantization, atomic spectra, mass hierarchy, and cosmological dynamics — emerge from the nonlinear self-consistent evolution of this field, without introducing auxiliary fundamental fields, external quantization postulates, or intrinsic entropy. The framework demonstrates that discrete physical spectra arise naturally from geometric stability conditions, yielding an emergent quantum description in the weak-field regime with an effective Schrödinger equation, an emergent Planck constant, and a geometrically induced Coulomb interaction. Particle masses appear as stable geometric resonances of ψ, providing a structural origin for the electron–proton mass ratio. On cosmological scales, the global relaxation of geometric tension in ψ reproduces the observed Hubble law, cosmological redshift, time dilation, surface brightness relations, and supernova distance–redshift behavior without invoking fundamental metric expansion or a cosmological constant. The macroscopic arrow of time arises from irreversible relaxation of ψ ensembles, while the underlying microscopic dynamics remain conservative and time-reversible. This framework offers a minimal, coherent geometric foundation for microphysics and cosmology within a single nonlinear field theory. IA assisted