Can weak lensing surveys confirm BICEP2?

The detection of B-modes in the cosmic microwave background (CMB) polarization by the BICEP2 experiment, if interpreted as evidence for a primordial gravitational wave background, has enormous ramifications for cosmology and physics. It is crucial to test this hypothesis with independent measurements. A gravitational wave background leads to B-modes in galaxy shape correlations (shear) both through lensing and tidal alignment effects. Since the systematics and foregrounds of galaxy shapes and CMB polarization are entirely different, a detection of a cross correlation between the two observables would provide conclusive proof for the existence of a primordial gravitational wave background. We find that upcoming weak lensing surveys will be able to detect the cross correlation between B-modes of the CMB and galaxy shapes. However, this detection is not sufficient to confirm or falsify the hypothesis of a primordial origin for CMB B-mode polarization.