Aether Cosmology XIII: Analytical Enclosure of Geff,max between 1.070 GN and 1.623 GN

Abstract

This paper completes the analytical derivation of the maximum gravitational amplification factor (Geff,max = 1.35 GN) within the TSTU/Aether cosmological framework. By isolating three distinct physical mechanisms from the single coupling parameter beta = 0.095, we demonstrate that the dynamics of the Aether are theoretically constrained: (0) the static coupling leading to 1.018 GN, (1) the kinetic memory of the scalar field at redshift z = 9 (1.070 GN), and (2) the linear perturbation induced by protogalactic collapse.

We identify a "Supra-Linear Overshoot" in which the linear approximation predicts an amplification of 1.623 GN, exceeding the target obtained from N-body simulations. This result is interpreted as analytical evidence for the existence of a non-linear damping mechanism (Vainshtein damping) that stabilizes galactic acceleration at the observed value of 1.35 GN.

This work concludes the series by providing a rigorous enclosure of the fifth force at the cosmic dawn.