Cylindrically symmetric inhomogeneous magnetized string cosmological model is investigated with cosmological term lambda varying with time. To get the deterministic solution, it has been assumed that the expansion (theta) in the model is proportional to the eigen value sigma1 1 of the shear tensor sigmai j. The value of cosmological constant for the model is found to be small and positive which is supported by the results from recent supernovae Ia observations. The physical and geometric properties of the model are also discussed in presence and absence of magnetic field.

In this paper general solutions are found for domain walls in Lyra geometry in the plane symmetric spacetime metric given by Taub. Expressions for the energy density and pressure of domain walls are derived in both cases of uniform and time varying displacement field beta. Some physical consequences of the models are also given. Finally, the geodesic equations and acceleration of the test particle are discussed.

FRW models of the universe have been studied in the cosmological theory based on Lyra's manifold. A new class of exact solutions has been obtained by considering a time dependent displacement field for variable deceleration parameter from which three models of the universe are derived (i) exponential (ii) polynomial and (iii) sinusoidal form respectively. The behaviour of these models of the universe are also discussed. Finally some possibilities of further problems and their investigations have been pointed out.