Weyl time evolution operator in planar Bianchi-type-I universes

Abstract

In this paper, Dirac’s equation in anisotropic Bianchi-type-I background spacetimes is treated with respect to orthonormal frames. By specializing to the massless spinor case and metrics with power-law scale factors and planar symmetry, an analytical expression of the approximate time evolution operator (TEO) is derived. By use of this operator, all approximate spinor solutions can be generated. By construction, these solutions agree asymptotically and at early times with the exact solutions. The operator approach is also well adapted for studying the case of small deviations from conformally flat backgrounds. In particular, it can be shown that the limiting case of vanishing anisotropy renders the correct result.