  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.
