The Cosmological Special Theory of Relativity (CSTR) re-derives the relativistic wave equations of quantum theory within an auxiliarycosmological inertial frame, in which a local, unexpanded spatial coordinate is related to the physically expanded coordinate of an expandingRobertson-Walker universe through a cosmological expansion function τ (t0) of the cosmological time t0 (Yi, 2020,?). This paper focusesspecifically on the quantum-theoretic content of that program: the cosmological Klein-Gordon equation, its plane-wave solutions, conservedcurrent, and Yukawa-potential solution (Yi, 2020, 2021); the non-relativistic Schr¨odinger limit and the associated cosmological positionmomentumand time-energy uncertainty relations (Yi, 2020); the Dirac equation in the cosmological inertial frame, its consistency with theKlein-Gordon equation, its non-relativistic (Pauli) reduction, and its negative-energy spectrum (Yi, 2021); the Klein-Gordon-Maxwell theoryof an interacting charged scalar and electromagnetic field, together with its gauge invariance and static Coulomb limit (Yi, 2021); and thecanonical quantization of the free Klein-Gordon field, including its Fock space, vacuum energy, and equal-time propagator (Yi, 2021, 2025).We conclude with a discussion of how this formalism compares with the treatment of quantum fields in curved and expanding spacetimes inthe mainstream literature, and with the open questions raised by an independent critical review of CSTR (A Critical Review, 2025).