A Dynamical Model of Temporal Expansion and Emergent Spacetime Geometry

This work presents a theoretical framework in which time is modeled as a dynamic scalar field , whose exponential expansion induces the emergence of spatial geometry and gravitational structure. Unlike classical general relativity, this model treats time as the generative origin of space. The proposed field equation leads to an exponentially expanding scale factor and a naturally arising curved spacetime, comparable to de Sitter or anti-de Sitter models. The theory provides new interpretations for cosmological acceleration and dark energy, while maintaining dimensional consistency and a potential link to quantum frameworks. Temporal Field, Emergent Spacetime, Scalar Field, General Relativity, Cosmology, Dark Energy, Quantum Gravityfg