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

TL;DR

This paper explores fermionic fields, including Grassmann variables, as potential sources of dark energy, demonstrating their compatibility with cosmological data and potential to address small-scale structure issues.

Contribution

It introduces a cosmological model with fermionic fields, including Grassmann variables, as dark energy sources, linking them to XCDM and w(z)CDM models, and analyzing their observational viability.

Findings

Fermionic fields can act as dark energy sources compatible with data.

Grassmannian fermions lead to vacuum-like equations of state.

Models may alleviate small-scale structure problems.

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 a massless fermionic field represented by a standard wave-function and the second one where a massive field is a Grassmann variable. {The first case naturally reduces to a XCDM model with a constant equation of state parameter, while the last case reproduces a $w(z)$CDM model for a massive field}, and in the massless limit, the intrinsic grassmannian property of the field leads always to a vacuum equation of state parameter, 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, BAO 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.