Cosmological Special Theory of Relativity: A Consolidated Review of the Formalism

Over a series of papers published between 2018 and 2025, the author has developed a framework, the Cosmological Special Theory of Relativity(CSTR), that incorporates the time-dependent expansion of the Robertson–Walker universe directly into the coordinate transformations,differential operators, and relativistic wave equations of special relativity, by way of an auxiliary “cosmological inertial frame” in whichphysical (expanded) coordinates are related to a local, unexpanded coordinate through a cosmological expansion function τ (t0) of the cosmologicaltime t0 (Yi, 2020,?). This paper consolidates the central results of that program into a single, self-contained review. We present thespace-time relations that define the cosmological inertial frame, the cosmological Klein-Gordon equation and its free-particle wave functionand Yukawa-potential solution (Yi, 2020, 2021), the corresponding non-relativistic Schr¨odinger limit and cosmological uncertainty relation,the Dirac equation in the cosmological inertial frame and its consistency with the Klein-Gordon equation (Yi, 2021), the Klein-Gordon–Maxwell theory of interacting complex scalar and electromagnetic fields (Yi, 2021), the canonical quantization of the Klein-Gordon scalarfield (Yi, 2021), the particle’s kinetic energy and force in the cosmological frame, and the extension to a Cosmological General Theory ofRelativity (CGTR), including cosmologically embedded Schwarzschild and Kerr-Newman solutions (Yi, 2021, 2025). We close with a discussionof the relationship between this formalism and the standard comoving-coordinate treatment of Robertson-Walker cosmology, and ofopen questions raised in the literature regarding CSTR’s consistency and standing (A Critical Review, 2025).