Constraining Parity Violation in Gravity with Measurements of
  Neutron-Star Moments of Inertia
  Neutron stars are sensitive laboratories for testing general relativity,
especially when considering deviations where velocities are relativistic and
gravitational fields are strong. One such deviation is described by dynamical,
Chern-Simons modified gravity, where the Einstein-Hilbert action is modified
through the addition of the gravitational parity-violating Pontryagin density
coupled to a field. This four-dimensional effective theory arises naturally
both in perturbative and non-perturbative string theory, loop quantum gravity,
and generic effective field theory expansions. We calculate here Chern-Simons
modifications to the properties and gravitational fields of slowly spinning
neutron stars. We find that the Chern-Simons correction affects only the
gravitomagnetic sector of the metric to leading order, thus introducing
modifications to the moment of inertia but not to the mass-radius relation. We
show that an observational determination of the moment of inertia to an
accuracy of 10%, as is expected from near-future observations of the double
pulsar, will place a constraint on the Chern-Simons coupling constant of
\xi^{1/4} < 5 km, which is at least three-orders of magnitude stronger than the
previous strongest bound.
