Physical Science: New Insights and Developments Vol. 5

Recent cosmological observations indicating an accelerated expansion of the Universe have renewed interest in models containing a positive cosmological constant (Λ). At the same time, anisotropic cosmological models have attracted attention as viable alternatives to the standard isotropic framework, particularly for understanding the early Universe and possible deviations from perfect isotropy. Motivated by the recent recognition of a positive value for the vacuum energy density and the realisation that a simple Kantowski Sachs model might fit the classical tests of cosmology, we study the qualitative behaviour of three anisotropic and homogeneous models: Kantowski–Sachs, Bianchi type-I, and Bianchi type-III universes with dust and a cosmological constant, to determine which models are physically permitted. We find that these models undergo isotropisation to the extent that observations cannot distinguish them from the standard model, except for the Kantowski–Sachs model (Ω_k0 < 0) and the Bianchi type-III model (Ω_k0 > 0) with Ω_Λ0 smaller than the critical value Ω_ΛM. Even if one imposes that the Universe should have been nearly isotropic since the last-scattering epoch (z ≈ 1000), meaning that it should have approximately equal Hubble parameters in all directions (considering the COBE four-year data), a large range of matterdensity parameters remains compatible with the Kantowski–Sachs and Bianchi type-III models if |Ω₀ +Ω_Λ0 −1| ≤ δ, for a very small δ. The Bianchi type-I model becomes exactly isotropic owing to our restrictions, and Ω₀ + Ω_Λ0 = 1 in this case. All these models approach a locally exponentially expanding state, provided that Ω_Λ > Ω_ΛM.