Chern-Simons Modified Gravity as a Torsion Theory and its Interaction with Fermions

TL;DR

This paper explores how Chern-Simons modified gravity introduces torsion, affects gyroscopic precession, and interacts with fermions, revealing new two-fermion interactions and potential observable effects.

Contribution

It demonstrates that CS modified gravity inherently produces torsion, couples with fermions to modify torsion, and introduces novel two-fermion interactions mediated by the CS term.

Findings

CS torsion vanishes only if the coupling is zero

Fermions enhance CS torsion effects

New two-fermion interactions mediated by axial currents

Abstract

We study the tetrad formulation of Chern-Simons (CS) modified gravity, which adds a Pontryagin term to the Einstein-Hilbert action with a spacetime-dependent coupling field. We first verify that CS modified gravity leads to a theory with torsion, where this tensor is given by an antisymmetric product of the Riemann tensor and derivatives of the CS coupling. We then calculate the torsion in the far field of a weakly gravitating source within the parameterized post-Newtonian formalism, and specialize the result to Earth. We find that CS torsion vanishes only if the coupling vanishes, thus generically leading to a modification of gyroscopic precession, irrespective of the coupling choice. Perhaps most interestingly, we couple fermions to CS modified gravity via the standard Dirac action and find that these further correct the torsion tensor. Such a correction leads to two new results: (i) a generic enhancement of CS modified gravity by the Dirac equation and axial fermion currents; (ii) a new two-fermion interactions, mediated by an axial current and the CS correction. We conclude with a discussion of the consequences of these results in particle detectors and realistic astrophysical systems.