Cosmic shear of the microwave background: The curl diagnostic

Weak-lensing distortions of the cosmic-microwave-background (CMB) temperature and polarization patterns can reveal important clues to the intervening large-scale structure. The effect of lensing is to deflect the primary temperature and polarization signal to slightly different locations on the sky. Deflections due to density fluctuations, gradient-type for the gradient of the projected gravitational potential, give a direct measure of the mass distribution. Curl-type deflections can be induced by, for example, a primordial background of gravitational waves from inflation or by second-order effects related to lensing by density perturbations. Whereas gradient-type deflections are expected to dominate, we show that curl-type deflections can provide a useful test of systematics and serve to indicate the presence of confusing secondary and foreground non-Gaussian signals.