The exact solutions of the field equations are obtained by using the gamma law equation of state p = (γ − 1)ρ in which the parameter γ depends on scale factor R. The fundamental form of γ (R) is used to analyze a wide range of phases in cosmic history: inflationary phase and radiation-dominated phase. The corresponding physical interpretations of cosmological solutions are also discussed in the framework of (n + 2) dimensional space time.

We consider a self-consistent system of Bianchi Type VI 0 cosmology and binary mixture of perfect fluid and dark energy. The perfect fluid is taken to be one obeying the usual equation of state p = γρ with γ ∈ [0, 1]. The dark energy is considered to be either the quintessence or Chaplygin gas. Exact solutions to the corresponding Einstein's field equations are obtained as a quadrature. Models with power-law and exponential expansion have discussed in detail.

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We have studied the interacting and non-interacting dark energy and dark matter in the spatially homogenous and anisotropic Bianchi type-I model in the Brans-Dicke theory of gravitation. The field equations have been solved (i) by using power-law relation and (ii) by assuming scale factor in terms of redshift. Here we have considered two cases of an interacting and non-interacting dark energy scenario and obtained general results. It has been found that for suitable choice of interaction between dark energy and dark matter we can avoid the coincidence problem which appears in the ΛCDM model. Some physical aspects and stability of the models are discussed in detail. The statefinder diagnostic pair, i.e., {r,s}, is adopted to differentiate our dark energy models.

The Kantowski–Sachs cosmological model for viscous generalized Chaplygin gas has been investigated in the Brans–Dicke theory of gravitation. To determine the solutions of field equations, we have considered the power-law relation for the average scale factor. We have computed some cosmological parameters and discussed their physical importance. Furthermore, we have discussed the nature of statefinder and [Formula: see text] diagnostics in our model. It is also worth noting that the conclusions of the cosmological parameter are consistent with modern observational data.