A new class of plane-symmetric inhomogeneous cosmological models of perfect fluid distribution with electro-magnetic field based on Lyra's geometry is obtained by considering a time dependent displacement field. The source of the magnetic field is due to an electric current produced along the z-axis. Only F 12 is a non-vanishing component of electromagnetic field tensor. To get the deterministic solutions, the free gravitational field is assumed to be of Petrov type-II non-degenerate. It has been found that the displacement vector β(t) behaves like cosmological term which is consistent with the recent observations of type Ia supernovae. It is also observed that β(t) affects entropy. Some geometric and physical behaviour of the models are also discussed in presence of magnetic field.

The present study deals with spatially homogeneous and locally rotationally symmetric (LRS) Bianchi type II cosmological models with bulk viscous fluid distribution of matter and decaying vacuum energy density . To get the deterministic models of the universe, we assume that the expansion (θ ) in the model is proportional to the shear (σ ). This leads to condition R = mS n , where R and S are metric potentials, m and n are constants. We have obtained two types of models of the universe for two different values of n. The vacuum energy density for both models is found to be a decreasing function of time and it approaches a small positive value at late time which is supported by recent results from the observations of (SN Ia). Some physical and geometric behaviour of these models are also discussed.