Fermionic wave functions and Grassmann fields as possible sources of dark energy

Abstract

We study a cosmological model with a fermionic field which can be interpreted as a source of dark energy in the universe. Two different approaches were considered, the first one with the fermion field represented by a standard wave-function and the second one where the field is a Grassmann variable. For this last case, in the massless limit, the intrinsic grassmannian property of the field leads always to a negative pressure contribution, irrespective the specific form of the potential. Both cases leads to a dark energy contribution of the fermionic sector. The models are totally compatible with recent cosmological data from Supernovae and Hubble parameter measurements. A brief study of linear evolution of density perturbations shows that some of the small scale problems related to standard model can be at least alleviated.