  Einstein-Cartan theory is an extension of the standard formulation of General
Relativity characterized by a non-vanishing torsion. The latter is sourced by
the matter fields via the spin tensor, and its effects are expected to be
important at very high spin densities. In this work we analyze in detail the
physics of Einstein-Cartan theory with Dirac and Maxwell fields minimally
coupled to the spacetime torsion. This breaks the $U(1)$ gauge symmetry, which
is suggested by the possibility of a torsion-induced phase transition in the
early Universe. The resulting Dirac-like and Maxwell-like equations are
non-linear with self-interactions as well as having fermion-boson non-minimal
couplings. We discuss several cosmological aspects of this theory, including
bounces, acceleration phases and matter-antimatter asymmetry in the torsion
era, as well as late-time effects such as the generation of an effective
cosmological constant, dark energy, and future bounces within cyclic solutions.
