Cross-Correlating Probes of Primordial Gravitational Waves

One of the most promising ways of detecting primordial gravitational waves generated during inflation is to observe B-modes of polarization, generated by Thomson scattering after reionization, in the cosmic microwave background (CMB). Large scale foregrounds though are expected to be a major systematic issue, so -- in the event of a tentative detection -- an independent confirmation of large scale gravitational waves would be most welcome. Previous authors have suggested searching for the analogous mode of cosmic shear in weak lensing surveys but have shown that the signal to noise of this mode is marginal at best. This argument is reconsidered here, accounting for the cross-correlations of the polarization and lensing B-modes. A lensing survey can potentially strengthen the argument for a detection of primordial gravitational waves, although it is unlikely to help constrain the amplitude of the signal.