The new spinor-unit field representation of the electromagnetism [ ] ( with quark and lepton sources ) is integrated via minimal coupling with standard Einstein gravitation , to formulate a Lagrangian model of the very early universe .
A completely new solution to the coupled Einstein-Maxwell equations , with sources , is derived .
These equations are generalized somewhat , but not in a way that violates any physical principles .

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 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 using an approach that is in marked contrast with the method followed to obtain a solution of the well known Friedmann model of a radiation-dominated universe .