Axially Symmetric Cosmological Models with Perfect Fluid and Cosmological Constant

Following recent considerations of a non-zero value for the vacuum energy density and the realization that a simple Kantowski-Sachs model might fit the classical tests of cosmology, we study the qualitative behavior of three anisotropic and homogeneous models: Kantowski-Sachs, Bianchi I and Bianchi III universes, with dust and cosmological constant, in order to find out which are physically permitted. In fact, these models undergo isotropisation, except for the Kantowski-Sachs model (Omega_{k_{0}}>0) with Omega_{Lambda_{0}}< Omega_{Lambda_{M}} and for the Bianchi III (Omega_{k_{0}}<0) with Omega_{Lambda_{0}}<Omega_{Lambda_{M}}, and the observations will not be able to distinguish between these models and the standard model. If we impose that the Universe should be very much isotropic since the last scattering epoch (z approximately 1000), meaning that the Universe should have approximately the same Hubble parameter in all directions, we are led to a matter density parameter very close to the unity at the present time.