Observational Predictions and Prospective Tests of the Cosmological Special Theory of Relativity

The Cosmological Special Theory of Relativity (CSTR) relates a local, unexpanded spatial coordinate to the physically expanded coordinate ofa Robertson-Walker universe through a cosmological expansion function τ (t0), and re-derives relativistic wave equations, electrodynamics,and general relativity within the resulting cosmological inertial frame (Yi, 2020, 2025). Companion reviews of this program have eachfound, for the specific quantities they consider – Yukawa interaction ranges and cross sections, Coulomb and hydrogen-like binding energies,Schwarzschild and Kerr-Newman horizon radii, parametrized post-Newtonian coefficients, and the fixed-epoch Lorentz transformation itself– that every physically measured quantity, once expressed in the physically expanded coordinate, recovers its ordinary, epoch-independentvalue, with the cosmological expansion function appearing only in the corresponding local-coordinate expression. This paper draws togetherthat recurring finding into an explicit observational assessment: because CSTR predicts no departure from ordinary physics for any processconfined to a single cosmological epoch, the theory is not constrained, but also not yet tested, by existing single-epoch observations, includingpresent bounds on the time-variation of the fine-structure constant and the proton-to-electron mass ratio from quasar absorption spectroscopy.We argue that a genuine test of CSTR requires a process that spans a cosmologically significant interval of time within a single observation– such as the redshift-drift (Sandage-Loeb) test, multi-epoch photon propagation, or cosmological particle creation – precisely the regimein which a companion review has shown that CSTR’s transformation law departs from a simple group structure. We summarize currentobservational bounds relevant to each sector of the theory and identify the redshift-drift test as the most concrete near-term observationalprogram capable of constraining CSTR’s genuinely multi-epoch predictions.