Noether symmetry for non-minimally coupled fermion fields

TL;DR

This paper explores a cosmological model with a non-minimally coupled fermion field, using Noether symmetry to determine potential functions, revealing the fermion field's dual role in inflation and dark matter.

Contribution

It introduces a method to determine potential and coupling functions via Noether symmetry in fermion-coupled gravity models, linking fermion behavior to cosmological phenomena.

Findings

Non-minimally coupled fermion acts as an inflaton causing accelerated expansion.

Minimally coupled fermion behaves as dark matter with decelerated expansion.

Noether symmetry constrains potential and coupling functions.

Abstract

A cosmological model where a fermion field is non-minimally coupled with the gravitational field is studied. By applying Noether symmetry the possible functions for the potential density of the fermion field and for the coupling are determined. Cosmological solutions are found showing that the non-minimally coupled fermion field behaves as an inflaton describing an accelerated inflationary scenario, whereas the minimally coupled fermion field describes a decelerated period being identified as dark matter.