Dynamical Behavior of Coupled Magnetized Dark Energy in Lyra's Geometry

The axially symmetric space-time with magnetized anisotropic generalized ghost pilgrim dark energy has been investigated in Lyra's geometry. To get a determinate solution, we considered that the expansion scalar theta in the model is proportional to shear scalar sigma. We found that the equation of state parameter of generalized ghost pilgrim dark energy behaves like a phantom dark energy. By stability analysis, our model was found to be stable. We have studied the correspondence between the models of generalized ghost pilgrim dark energy and polytropic gas dark energy. Accordingly, the potential and dynamics of the scalar field of the polytropic gas is reconstructed. Moreover, we have calculated various physical and kinematical parameters of the model and observed that these are compatible with recent observations.