Torsion, Dirac Field, Dark Matter and Dark Radiation

TL;DR

This paper explores how torsion and a scalar field in Riemann-Cartan geometry can naturally account for dark matter and dark radiation, with a focus on Dirac fields and gauge connections.

Contribution

It introduces a novel Lagrangian density derived from the SO(4,1) Pontryagin density, linking the scalar field to Dirac field dimensions and proposing it as a candidate for dark matter and dark radiation.

Findings

Scalar field linked to Dirac field dimension

Field equations show non-interacting scalar and Dirac fields

Scalar field emerges as a natural dark matter and dark radiation candidate

Abstract

The role of torsion and a scalar field $\phi$ in gravitation, especially, in the presence of a Dirac field in the background of a particular class of the Riemann-Cartan geometry is considered here. Recently, a Lagrangian density with Lagrange multipliers has been proposed by the author which has been obtained by picking some particular terms from the SO(4,1) Pontryagin density, where the scalar field $\phi$ causes the de Sitter connection to have the proper dimension of a gauge field. In this article the scalar field has been linked to the dimension of the Dirac field. Here we get the field equations for the Dirac field and the scalar field in such a way that both of them appear to be mutually non-interacting. In this scenario the scalar field appears to be a natural candidate for the dark matter and the dark radiation.