String Cosmological Model in Cylindrically Symmetric Inhomogeneous Universe with Electromagnetic Field

Cylindrically symmetric inhomogeneous string cosmological models in presence of electromagnetic field is investigated. We have assumed that $F_{12}$ is the only non-vanishing component of $F_{ij}$. The Maxwell’s equations require that $F_{12}$ is the function of $x$ and $t$ both and the magnetic permeability is the function of $x$ and $t$ both. To get the deterministic solution, it has been assumed that the expansion ($\theta$) in the model is proportional to the eigen value ${\sigma }_1^1$ of the shear tensor ${\sigma }_j^i$. The derived model represents the inflationary scenario as the proper volume increases exponentially with cosmic time. It is observed that the model has a point type singularity. The physical and geometric aspects of the model are also discussed.