In this paper, we have studied Bianchi type-I string cosmological model by combining Kaluza-Klein (KK) theory and theory of gravity which is an extension of 5-dimensional KK string cosmological models. We have used equation of state in the form of p-string or Takabayasi string given by 1 , where ρ and λ denote the rest density of energy cloud of strings, and the tension density of the system of strings, respectively and ω is a constant. In order to get physically significant and viable solution various forms of the function are assumed, in this paper we assume (e.g. Astashenok et al. (2017) [1] ), where α is real number. Some physical and geometrical properties of the model are also discussed.

An exact solution of the vacuum Einstein field equations (VE-FEs) has been obtained of a spatially homogeneous and anisotropic (SHA) Bianchi type-I cosmological model by Kasner. The Kasner metric is shown to be a special case, and the exact vacuum solution of Kasner form model is obtained. Some physical properties of the model have been discussed.

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In this paper, we attempt to study spatially homogeneous Bianchi types-III, V, VI 0 & VI h cosmological models in f (R, T) theory of gravity. Here the models are obtained by assuming forms of the function f (R, T) as f (R, T) = R + 2 f (T) and f (R, T) = f 1 (R) + f 2 (T). The exact solutions of Einstein's field equations (EFEs) have been obtained for two different types of physically viable cosmologies using a special form of Hubble parameter (HP). The physical and geometrical properties of these models have been discussed and expressions for the Ricci scalar R in each case are obtained.