Kantowaski space time in the presence of mass less scalar field with a flat potential is investigated. To obtain an inflationary universe, we have considered a flat region in which V is constant. Some physical properties of the model are also discussed.

Bianchi type-I massive string cosmological model for perfect fluid distribution in the presence of magnetic field is investigated in Rosen's [Gen. Relativ. Gravit. 4, 435 (1973)] bimetric theory of gravitation. To obtain the deterministic model in terms of cosmic time, we have used the condition A = (BC) n , where n is a constant, between the metric potentials. The magnetic field is due to the electric current produced along the x-axis with infinite electrical conductivity. Some physical and geometrical properties of the exhibited model are discussed and studied.

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Abstract. In the present study we investigate, Hypersurface-Homogeneous cosmological model in f(R,T) theory of gravity with a term Λ. We obtain the gravitational field equations in the metric formalism, which follow from the covariant divergence of the stress-energy tensor. The field equations correspond for a specific choice of f(R,T)=f 1 (R)+f 2 (T), with the individual superior functions f 1 (R)=λR and f 2 (T)=λT. In this paper, we consider a simple form of expansion history of Universe referred to as the hybrid expansion law − a product of power-law and exponential type of functions. Einstein's field equations have been solved by taking into account the hybrid expansion law for scale factor that yields time dependent deceleration parameter (DP). Some physical and geometric properties of the model along with physical acceptability of the solutions have also been discussed in detail.

In this paper, we have obtained the solutions of perfect fluid cosmological model in Cylindrically-symmetric space time (Marder in Proc. R. Soc. A 246:133, 1958) with varying cosmological constant in the presence of electromagnetic field. To get determinate model of the universe we assumed that the scalar of expansion in the model is proportional to the eigen-value of the shear tensor which lead to the condition A = (BC) n . The magnetic field is due to an electric current produced along x-axis. Thus the magnetic field is in yz-plane and F 23 is the only non-vanishing component of electromagnetic field tensor F ij . Various physical and geometrical features of the model have been discussed.