Causal Saturation of Linear Gravitational Growth in Relativistic Cosmology

This work establishes a model-independent causal saturation bound on linear gravitational growth in relativistic cosmology. Using only the hyperbolic structure of the perturbation equations and the finiteness of the cosmological horizon, we demonstrate that unlimited linear growth is mathematically forbidden in any causal Friedmann–Robertson–Walker spacetime. The result functions as a structural consistency constraint, independent of phenomenological modeling or observational fitting.