Parametrized post-Newtonian expansion of Chern-Simons gravity

We investigate the weak-field, post-Newtonian (PN) expansion to the solution of the field equations in Chern-Simons (CS) gravity with a perfect fluid source. In particular, we study the mapping of this solution to the parametrized post-Newtonian (PPN) formalism to 1 PN order in the metric. We find that the PPN parameters of Chern-Simons gravity are identical to those of general relativity, with the exception of the inclusion of a new term that is proportional to the Chern-Simons coupling parameter and the curl of the PPN vector potentials. We also find that the new term is naturally enhanced by the nonlinearity of spacetime and we provide a physical interpretation for it. By mapping this correction to the gravito-electromagnetic framework, we study the corrections that this new term introduces to the acceleration of point particles and the frame-dragging effect in gyroscopic precession. We find that the CS correction to these classical predictions could be used by current and future experiments to place bounds on intrinsic parameters of Chern-Simons gravity and, thus, string theory.