Gravitational-wave probe of effective quantum gravity

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 loop quantum gravity-require modification of the classical Einstein-Hilbert action for the spacetime metric by the addition of a parity-violating Chern-Simons term. The introduction of such a term leads to spacetimes that manifest an amplitude birefringence in the propagation of gravitational waves. While the degree of birefringence may be intrinsically small, its effects on a gravitational wave accumulate as the wave propagates. Observation of gravitational waves that have propagated over cosmological distances may allow the measurement of even a small birefringence, providing evidence of quantum gravitational effects. 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 coupling may be found. Here we evaluate the effect of a Chern-Simons induced spacetime birefringence to the propagation of gravitational waves from such systems. Focusing attention on the gravitational waves from coalescing binary black holes systems, which LISA will be capable of observing at redshifts approaching 30, we find that the signature of Chern-Simons gravity is 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 magnitude of change reflecting the integrated history of the Chern-Simons coupling over the worldline of the radiation wave front. 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 real effect are different than the apparent effect produced by Chern-Simons birefringence, allowing the two effects to be separately identified. In this way gravitational-wave observations with LISA may thus provide our first and only opportunity to probe the quantum structure of spacetime over cosmological distances.