Spinor-Unit Field Representation of Electromagnetism Applied to a Model Inflationary Cosmology

The new spinor-unit field representation of the electromagnetism \cite{Nash2010} (with quark and lepton sources) is integrated via minimal coupling with standard Einstein gravitation, to formulate a Lagrangian model of the very early universe. The solution of the coupled Euler-Lagrange field equations yields a scale factor $a(t)$ (comoving coordinates) that initially exponentially increases $N$ e-folds from $a(0) \approx 0$ to $a_{1} = a(0) {e}^{N}$ ($N$ = 60 is illustrated), then exponentially decreases, then exponentially increases to $a_{1}$, and so on almost periodically. (Oscillatory cosmological models are not knew, and have been derived from string theory and loop quantum gravity.) It is not known if the scale factor escapes this periodic trap. This model is noteworthy in several respects: $\{1\}$ All fundamental fields other than gravity are realized by spinor fields. $\{2\}$ A plausible connection between the \emph{unit} field $\mathbf{u}$ and the generalization of the photon wave function with a form of Dark Energy is described, and a simple natural scenario is outlined that allocates a fraction of the total energy of the Universe to this form of Dark Energy. $\{3\}$ A solution of an analog of the pure Einstein-Maxwell equations is found. This approach is in contrast with the method followed to obtain a solution of the well known Friedmann model of a radiation-dominated universe.