Geometric Acceleration without Matter: The Psi-Invariant and the Self-Soursing Structure of Spacetime

This paper presents a novel geometric theory of cosmic acceleration, where the observed acceleration of the universe is explained by a new geometric invariant, the Psi-connection (Ψ). This invariant modifies the dynamics of spacetime without requiring external matter fields. The work also proposes empirical verification methods using cosmological data such as the cosmic microwave background (CMB), large-scale structure surveys, and Hubble parameter measurements.