A Unified Geometric Framework: Emergent Gravity, Matter, and Dark Sectors from a Recursive Geometric Field

This work presents a unified geometric framework in which gravity, matter, and dark sector phenomena emerge as effective regimes of a Recursive Geometric Field (RGF). Rather than introducing new particles, dynamical fields, or modifications to the Einstein–Hilbert action, the RGF is defined as a non-dynamical, phenomenological geometric structure that encodes the large-scale recursive organization of spacetime. Within this picture, familiar cosmological phenomena are interpreted as scale-dependent manifestations of geometry, while local gravitational physics remains fully consistent with General Relativity. Late-time cosmic acceleration arises naturally from an effective geometric expansion law governed by a single dimensionless parameter, without invoking a cosmological constant or dynamical dark energy. Matter perturbations evolve according to the standard linear growth equation, with the RGF entering only through the background expansion history. The resulting growth of structure exhibits a mild, scale-independent suppression relative to ΛCDM, consistent with current redshift-space distortion measurements and well within observational uncertainties. Dark matter and dark energy are thus reinterpreted not as fundamental substances, but as effective geometric phenomena associated with different regimes of the recursive spacetime structure. The framework is explicitly phenomenological and limited to late-time cosmology, but it is falsifiable through precise measurements of structure growth, consistency relations between expansion and growth, and future large-scale surveys. The RGF offers a conceptually economical alternative perspective in which cosmic acceleration and structure formation share a common geometric origin.