In cosmological special relativity theory, we study Maxwell equations, electromagnetic wave equations and functions. In the cosmological special theory of relativity, we study energymomentum relations, the Klein-Gordon equation and wave functions. We study Yukawa’s potential dependence on time in a cosmological inertial frame. If we solve the Klein-Gordon equation, we obtain the Yukawa potential dependent on time in the cosmological inertial frame. The Schrodinger equation is a wave equation. The wave function used as a probability amplitude in quantum mechanics. We make the Schrodinger equation from Klein-Gordon free particle’s wave function in the cosmological special theory of relativity. The Dirac equation is a one order wave equation. The wave function used as a probability amplitude in quantum mechanics. We make the Dirac equation from the wave function, Type A in the cosmological inertial frame. The Dirac equation satisfies the Klein-Gordon equation in the cosmological inertial frame. We found equations of complex scalar fields and electromagnetic fields on the interaction of complex scalar fields and electromagnetic fields in Klein-Gordon-Maxwell theory from Type A of the wave function and Type B of the expanded distance in the cosmological inertial frame. In the cosmological special theory of relativity, we quantized the Klein-Gordon scalar field. We treat Lagrangian density and Hamiltonian in a quantized Klein-Gordon scalar field. We address the particle’s force and kinetic energy in the cosmological special theory of relativity. In expanded universe, wefound gravity field equation and solution. We found Schwarzschild solution, Kerr-Newman solution in expanded universe. Hence, We found new general relativity theory-Cosmological General Theory of Relativity(CGTR).