The present study deals with locally rotationally symmetric (LRS) Bianchi type II cosmological model representing massive string. The energy-momentum tensor for such string as formulated by Letelier (Phys. Rev. D 28:2414, 1983) is used to construct massive string cosmological model for which we assume that the expansion (θ ) in the model is proportional to the shear (σ ). This condition leads to A = B m , where A and B are the metric coefficients and m is proportionality constant. For suitable choice of constant m, it is observed that in early stage of the evolution of the universe string dominates over the particle whereas the universe is dominated by massive string at the late time. Our model is in accelerating phase which is consistent to the recent observations of type Is supernovae. Some physical and geometric behavior of the model is also discussed.

A plane-symmetric magnetized inhomogeneous cosmological model of the universe with time dependent gauge function β for perfect fluid distribution with variable magnetic permeability within the framework of Lyra geometry is investigated. The source of the magnetic field is due to an electric current produced along the z-axis. Thus F 12 is the only non-vanishing component of electromagnetic field tensor F ij . To get a deterministic solution of Einstein's modified field equations, the free gravitational field is assumed to be Petrov type-II non-degenerate. For our derived model we obtain the deceleration parameter q = −1 as in the case of de Sitter universe. It has been found that the displacement vector β(t) behaves like cosmological term in the normal gauge treatment and the solution is consistent with the observations. The displacement vector β(t) affects entropy. Some physical and geometric properties of the model are also discussed.