  General relativity (GR) predicts concordant trajectories for photons and
gravitational waves (GW). We propose a new multi-messenger avenue (GW-CMB-CMB)
to prove this aspect of fundamental physics by cross-correlating the GW signal
of astrophysical origin with the lensing field derived from the cosmic
microwave background (CMB). This new window will allow robust measurement of
the prediction from GR with high signal-to-noise and will be able to unveil the
true nature of gravity using the GW sources detected by missions such as the
Laser Interferometer Space Antenna (LISA), Einstein Telescope and Cosmic
Explorer.
