On the Dirac field in the Palatini form of 1/R gravity

TL;DR

This paper investigates the Dirac field coupled to 1/R gravity in the Palatini formalism, allowing the connection in the Dirac action to be independent, leading to a significantly different and more complex theory.

Contribution

It introduces a novel approach by treating the connection in the Dirac action as independent, contrasting with previous work that used the Christoffel symbol.

Findings

The resulting theory differs substantially from previous models.

Allowing the connection to be independent complicates the theory.

The approach opens new avenues for understanding gravity-fermion couplings.

Abstract

In recent papers (astro-ph/0306630, gr-qc/0312041) I have argued that the observed cosmological acceleration can be accounted for by the inclusion of a 1/R term in the gravitational action in the Palatini formalism. Subsequently, Flanagan (astro-ph/0308111, gr-qc/0403063) argued that this theory is equivalent to a scalar-tensor theory which produces corrections to the standard model that are ruled out experimentally. In this article I examine the Dirac field coupled to 1/R gravity. The Dirac action contains the connection which was taken to be the Christoffel symbol, not an independent quantity, in the papers by Flanagan. Since the metric and connection are taken to be independent in the Palatini approach it is natural to allow the connection that appears in the Dirac action to be an independent quantity. This is the approach that is taken in this paper. The resulting theory is very different and much more complicated than the one discussed in Flanagan's papers.