The spin connection, the Dirac and the Einstein-Dirac equation in Robertson-Walker space-time

The Dirac equation in the spin connection formulation is studied in the Robertson-Walker space-time. The spin connection components are explicitly obtained from a suitable choice of a tetrad frame after a preliminary calculation of the spin rotation coefficients. The knowledge of the spin connection gives a simple tensor form to the Dirac equation and facilitates the translation of the theory into the language of the Newman-Penrose formalism. It also provides the basic elements to determine a particular solution of the equations that describe the interaction of the gravitational and the Dirac field in Robertson-Walker space-time.