The Bianchi type-IX cosmological model with variable ω has been studied in the scalar tensor theory of gravitation proposed by Saez and Ballester [Phys. Lett. A 113: 467, 1985] in the presence and absence of magnetic field of energy density ρ b. A special law of variation of Hubble's parameter proposed by Berman [Nuovo Cimento 74 B, 182, 1983] has been used to solve the field equations. The physical and kinematical properties of the model are also discussed.

The new Bianchi type-IX cosmological models with binary mixture of perfect fluid and anisotropic dark energy have been studied. The unique solution of field equations is obtained by assuming that the energy conservation equation of the perfect fluid and dark energy vanishes separately together with a special law for the mean Hubble parameter (Berman, 1983) which yields a constant value of the deceleration parameter and generates two types of solutions, one is of power law type and other is of the exponential type. To have a general description of an anisotropic dark energy component in terms of its equation of state) (de  , a skewness parameters  have been introduced. The statefinder diagnostic pair (i.e.   s r, parameter) is used to characterize different phases of the universe. The various geometric and kinematic properties of the model and the behavior of the anisotropy of the dark energy have been discussed.

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Bianchi type-IX cosmological models with variable equation of state (EoS) parameter have been investigated in general relativity when universe is filled with dark energy. The field equations have been solved by considering (i) q B = (variable); (ii) q kt m 1 = − + − , where k and m are constants; (iii) 2 1 = − +. This renders early decelerating and late time accelerating cosmological models. The physical and geometrical properties of the models are also discussed.

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