Inflation and Singularity in Einstein–Cartan Theory

Within the framework of Einstein–Cartan theory, we obtain a general condition leading to singularity and inflation for all Bianchi cosmological models. If the spin energy is smaller than anisotropic energy density (i.e. S²−σ²≤0), the Universe can not avoid singularity. If S²−σ²>-ρ_v/2 (ρ_v is vacuum energy density), the Universe can undergo an inflation phase. Examples of Bianchi type−IX, I and V cosmological models are discussed.