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Inhomogeneous Perfect Fluid Universe with Electromagnetic Field in Lyra Geometry

A new class of cylindrically symmetric inhomogeneous cosmological models for perfect fluid distribution with electromagnetic field is obtained in the context of Lyra's geometry. We have obtained two types of solutions by considering the uniform as well as 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 solution, it has been assumed that the expansion $θ$ in the model is proportional to the shear $σ$. It has been found that the solutions are consistent with the recent observations of type Ia supernovae and the displacement vector $β(t)$ affects entropy. Physical and geometric aspects of the models are also discussed in presence and absence of magnetic field.