A gravitational-wave probe of effective quantum gravity

The Green-Schwarz anomaly-cancelling mechanism in string theories requires a Chern-Simons term in the Einstein-Hilbert action, which leads to an amplitude birefringence of spacetime for the propagation of gravitational waves. While the degree of birefringence may be intrinsically small, its effects on a gravitational wave will accumulate as the wave propagates. The proposed Laser Interferometer Space Antenna (LISA) will be sensitive enough to observe the gravitational waves from sources at cosmological distances great enough that interesting bounds on the Chern-Simons may be found. Here we evaluate the effect of a Chern-Simons induced spacetime birefringence to the propagation of gravitational waves from such systems. We find that gravitational waves from in coalescing binary black hole system are imprinted with a signature of Chern-Simons gravity. This signature appears as a time-dependent change in the apparent orientation of the binary's orbital angular momentum with respect to the observer line-of-sight, with the change magnitude reflecting the integrated history of the Chern-Simons coupling over the worldline of a radiation wavefront. While spin-orbit coupling in the binary system will also lead to an evolution of the system's orbital angular momentum, the time dependence and other details of this \emph{real} effect are different than the \emph{apparent} effect produced by Chern-Simons birefringence, allowing the two effects to be separately identified.