  All modern routes leading to a quantum theory of gravity -- i.e.,
perturbative quantum gravitational one-loop exact correction to the global
chiral current in the standard model, string theory, and perhaps even loop
quantum gravity -- require supplementing the Einstein-Hilbert action with a
parity-violating Chern-Simons term. Such a term leads to amplitude-birefringent
gravitational wave propagation: i.e., one (circular) polarization state
amplified with propagation while the other is attenuated. The proposed Laser
Interferometer Space Antenna (LISA) is capable of observing gravitational wave
sources at cosmological distances, suggesting the possibility that LISA
observations may place a strong bound on this manifestation of quantum gravity.
Here we report on a calculation of the effect that spacetime amplitude
birefringence has on the signal LISA is capable of observing from inspiraling
supermassive black hole binaries at large redshift. We find that the
birefringence manifests itself in the observations as an anomalous precession
of the binary's orbital angular momentum as it evolves toward coalescence,
whose magnitude depends on the integrated history of the Chern-Simons coupling
over the worldline of radiation wavefront. We estimate that LISA could place
bounds on Chern-Simons modified gravity that are several orders of magnitude
stronger than the present Solar System constraints, thus providing a probe of
the quantum structure of spacetime.
