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In this work we explore the boundary conditions in the Einstein-Hilbertaction, by considering a displacement from the Riemannian manifold to anextended one. The latter is characterized by including spinor fields into thequantum geometric description of a noncommutative spacetime. These fields aredefined on the background spacetime, emerging from the expectation value of thequantum structure of spacetime generated by matrices that comply with aClifford algebra. We demonstrate that spinor fields are candidate to describeall known interactions in physics, with gravitation included. In this frameworkwe demonstrate that the cosmological constant $\Lambda$, is originatedexclusively by massive fermion fields that would be the primordial componentsof dark energy, during the inflationary expansion of an universe that describesa de Sitter expansion.

Fermionic origin of dark energy in the inflationary universe from Unified Spinor Fields