A framework to a mass-dimension-one fermionic sigma model

In this paper a mass-dimension-one fermionic sigma model, realized by the eigenspinors of the charge conjugation operator with dual helicity (Elko spinors), is developed. Such spinors are chosen as a specific realization of mass-dimension-one spinors, wherein the non-commutative fermionic feature is ruled by torsion. Moreover, we analyse Elko spinors as a source of matter in a background in expansion and we have found that such kind of mass-dimension-one fermions can serve not only as dark matter but they also induce an effective cosmological constant.