Chern-Simons modified gravity as a torsion theory and its interaction with fermions

Stephon Alexander, Nicolás Yunes

Research output: Contribution to journalArticlepeer-review


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 interaction, 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.

Original languageEnglish (US)
Article number124040
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number12
StatePublished - Jun 24 2008
Externally publishedYes

ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)


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