Separation of variables and exact solution to Dirac and Weyl equations in Robertson–Walker space-times

Abstract

In this paper the separation of variables is presented in the Dirac equation in open, flat, and closed expanding cosmological Robertson–Walker universes. The equations governing the radial variable and the evolution of the time-dependent factor are obtained. An exact solution to the Weyl equation is derived for an arbitrary expansion factor of the Robertson–Walker metrics. An exact solution to Dirac equation in a universe filled with radiation is also presented.