Structure Growth on an Effective Geometric Expansion Background

This paper follows a simple but necessary line of reasoning: if late–time cosmic acceleration comes from geometry rather than a new energy component, then that same geometric expansion must also allow structures to form in a sensible way. Within the Recursive Geometric Field (RGF) framework, the expansion history is treated as an effective geometric background fixed by observations, while gravity at local scales remains unchanged. No new fields are added, no modifications to the Einstein–Hilbert action are introduced, and dark energy is not assumed as a fundamental substance. Using this geometric expansion law, the standard linear growth equation for matter perturbations is solved in the late–time universe.…