  It is assumed that the non-singular big-bang birth of the Universe as set
forth by Einstein-Cartan's theory particularly brought about the appearance of
the cosmic microwave and dark energy backgrounds, dark matter, gravitons as
well as of Dirac particles. On account of this assumption, a two-component
description of the motion of quarks and leptons prior to the occurrence of
hadronization is presented within the framework of the torsionful
{\epsilon}-formalism of Infeld and van der Waerden. The relevant field
equations are settled on the basis of the implementation of conjugate minimal
coupling covariant derivative operators that carry additively typical
potentials for the cosmic backgrounds such as geometrically specified in a
previous work. It appears that the derivation of the wave equations which
control the spacetime propagation of Dirac fields at very early stages of the
cosmic evolution, must be tied up with the applicability of certain subsidiary
relations. The wave equations themselves suggest that quarks and leptons
interact not only with both of the cosmic backgrounds, but also with dark
matter. Nevertheless, it becomes manifest that the inner structure of the
framework allowed for does not give rise at all to any interaction between
gravitons and Dirac particles. The overall formulation ascribes an
intrinsically non-geometric character to Dirac's theory, in addition to
exhibiting a formal evidence that dark energy and dark matter must have
partaken of a cosmic process of hadronization.
