In cosmological special relativity theory, we study Maxwell equations, electromagnetic wave equations and functions. In the cosmological special theory of relativity, we study energy?momentum relations, the Klein-Gordon equation and wave functions. If we solve the Klein?Gordon equation, we obtain the Yukawa potential in the cosmological inertial frame. We derive the Schrodinger equation from Klein-Gordon free particle’s wave function in the cosmological special theory of relativity. We derive the uncertainty principle in cosmological quantum mechanics in cosmological special relativity theory. The Dirac equation is a one order wave equation. The wave function is used as a probability amplitude in quantum mechanics. We derive 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 the 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 the expanded universe, we found the gravity field equation and solution. We found the Schwarzschild solution and Kerr-Newman solution in an expanded universe. Hence, we found a new general relativity theory-the Cosmological General Theory of Relativity (CGTR).