  In this work we explore the boundary conditions in the Einstein-Hilbert
action, by considering a displacement from the Riemannian manifold to an
extended one. The latter is characterized by including spinor fields into the
quantum geometric description of a noncommutative spacetime. These fields are
defined on the background spacetime, emerging from the expectation value of the
quantum structure of spacetime generated by matrices that comply with a
Clifford algebra. We demonstrate that spinor fields are candidate to describe
all known interactions in physics, with gravitation included. In this framework
we demonstrate that the cosmological constant $\Lambda$, is originated
exclusively by massive fermion fields that would be the primordial components
of dark energy, during the inflationary expansion of an universe that describes
a de Sitter expansion.
