Plane symmetric cosmological models

In the present work, we execute the Lie symmetry analysis on the Einstein-Maxwell field equations in the plane symmetric spacetime. Under the background of the plane symmetric space-time we compute the Lie point symmetries, perform the similarity reductions and obtain exact solutions in connection to the evolutionary scenario of the universe. The special feature of the study is that it deals with the electromagnetic energy of the inhomogeneous universe through the non-vanishing component of electromagnetic field tensor $F_{12}$ and assumes that the free gravitational field is of Petrov type-II non-degenerate. We have found that the electromagnetic field tensor is positive and increasing function of time. To validate the solution set, we examine with detailed discussions several physical as well as geometrical features of a specific sub-case of the model.