On solutions of the Pauli equation in non-static de Sitter metrics

A particle with spin 1/2 is investigated both in expanding and oscillating cosmological de Sitter models. It is shown that these space-time geometries admit existence of the non-relativistic limit in the covariant Dirac equation. Procedure for transition to the Pauli approximation is conducted in the equations in the variables $(t, r)$, obtained after separating the angular dependence of $(θ, ϕ)$ from the wave function. The non-relativistic systems of equations in the variables $(t, r)$ is solved exactly in both models. The constructed wave functions do not represent stationary states with fixed energy, however the corresponding probability density does not depend on the time.

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