An exact solution of Dirac's equation in an open Robertson-Walker univ
erse is constructed such that the corresponding energy-momentum densit
y T(mu nu) obeys the cosmological principle. However, in an open unive
rse, this principle must always be violated by the other physical dens
ities of the cosmological solution (e.g. pseudoscalar, (axial-) curren
t and polarization). If the current density j(mu) = psiBARgamma(mu)PSI
is required to obey the cosmological principle, then the universe mus
t be flat.