Dirac spinors and their application to Bianchi-I space-times in 5 dimensions

TL;DR

This paper explores five-dimensional Einstein--Cartan spacetimes with Dirac spinor fields, analyzing their properties and potential to induce inflation or dark energy in Bianchi-I cosmological models.

Contribution

It provides a detailed comparison of Dirac spinors in five and four dimensions and applies this to study their role in cosmological evolution in five-dimensional Bianchi-I models.

Findings

Dirac spinors in five dimensions lack chiral projections unlike in four dimensions

The study assesses the potential of five-dimensional Dirac fields to drive inflation or dark energy

Polar decomposition highlights key similarities and differences between 4D and 5D spinors

Abstract

We consider a five-dimensional Einstein--Cartan spacetime upon which Dirac spinor fields can be defined. Dirac spinor fields in five and four dimensions share many features, like the fact that both are described by four-component spinor fields, but they are also characterized by strong differences, like the fact that in five dimensions we do not have the possibility to project on left-handed and right-handed chiral parts unlike what happens in the four-dimensional instance: we conduct a polar decomposition of the spinorial fields, so to highlight all similarities and discrepancies. As an application of spinor fields in five dimensions, we study Bianchi-I spacetimes, verifying whether the Dirac fields in five dimensions can give rise to inflation or dark-energy dominated cosmological eras or not.