Noether gauge symmetry of Dirac field in $2+1$ dimensional gravity

TL;DR

This paper explores a $2+1$ dimensional gravity model with a non-minimally coupled Dirac field, using Noether gauge symmetry to determine coupling functions, leading to cosmological solutions that suggest early inflation and late acceleration.

Contribution

It introduces a method to determine coupling functions in $2+1$ dimensional gravity with Dirac fields via Noether gauge symmetry, revealing cosmological implications.

Findings

Cosmological solutions show early inflation.

Solutions indicate late-time acceleration.

Noether gauge symmetry fixes coupling functions.

Abstract

In this paper, we consider a gravitational theory including a Dirac field that is non-minimal coupled to gravity in $2+1$ dimensions. Noether gauge symmetry approach can be used to fix the form of coupling function $F(\Psi)$ and the potential $V(\Psi)$ of the Dirac field and to obtain a constant of motion for the dynamical equations. In the context of $2+1$ dimensions gravity, we investigate cosmological solutions of the field equations using these forms obtained by the existent of Noether gauge symmetry. In this picture, it is shown that for the non-minimal coupling case, the cosmological solutions indicate both an early-time inflation and late-time acceleration for the universe.