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

Patrick L. Nash
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