Bianchi type-II cosmological model: some remarks

Within the framework of Bianchi type-II (BII) cosmological model the behavior of matter distribution has been considered. It is shown that the non-zero off-diagonal component of Einstein tensor implies some severe restriction on the choice of matter distribution. In particular for a locally rotationally symmetric Bianchi type-II (LRS BII) space-time it is proved that the matter distribution should be strictly isotropic if the corresponding matter field possesses only non-zero diagonal components of the energy-momentum tensor.