A modified theory of gravity with torsion and its applications to cosmology and particle physics

TL;DR

This paper develops a comprehensive gravity theory incorporating both curvature and torsion, applying it to analyze self-interactions of ELKO and Dirac fields, with implications for cosmology and particle physics.

Contribution

It introduces a general least-order derivative gravity theory with independent torsion and curvature, exploring its effects on spinor fields and their self-interactions.

Findings

Torsion coupling constants influence spinor self-interactions.

ELKO and Dirac fields exhibit non-linearities depending on torsion coupling.

Potential subatomic scale effects of spinor self-interactions are discussed.

Abstract

In this paper we consider the most general least-order derivative theory of gravity in which not only curvature but also torsion is explicitly present in the Lagrangian, and where all independent fields have their own coupling constant: we will apply this theory to the case of ELKO fields, which is the acronym of the German \textit{Eigenspinoren des LadungsKonjugationsOperators} designating eigenspinors of the charge conjugation operator, and thus they are a Majorana-like special type of spinors; and to the Dirac fields, the most general type of spinors. We shall see that because torsion has a coupling constant that is still undetermined, the ELKO and Dirac field equations are endowed with self-interactions whose coupling constant is undetermined: we discuss different applications according to the value of the coupling constants and the different properties that consequently follow. We highlight that in this approach, the ELKO and Dirac field's self-interactions depend on the coupling constant as a parameter that may even make these non-linearities manifest at subatomic scales.