Cosmological principle and primordial spinor fields

An exact solution of Dirac's equation in an open Robertson-Walker universe is constructed such that the corresponding energy-momentum densityT _µv obeys the cosmological principle. However, in anopen universe, this principlemust always be violated by the other physical densities of the cosmological solution (e.g. pseudoscalar, (axial-) current and polarization). If the current densityj _µ = isrequired to obey the cosmological principle, then the universe must beflat.