Non-relativistic description for a spin 1 particle in expanding De Sitter universe
For expanding de Sitter space-time, a spin 1 particle is investigated in the non-relativistic Pauli approximation. After separation of the variables in the relativistic Duffin-Kemmer-Petiau equation, the procedure of non-relativistic approach is performed for the system of 10 equations in the variables (t, r). As a result, the problem reduces to three second-order related differential equations. Requirement of diagonalization of the parity operator allows the system to be split into (1 + 2) subsystems. The fourth-order equations obtained are solved with the help of the factorization method, which permits the problem to be reduced to the analysis of second-order equations. In this way, the Pauli equation for a spin 1 particle in the expanding De Sitter universe is solved exactly: three series of states and the relevant rules of quantization of the spectral parameter are obtained.