New Probe of Inflationary Gravitational Waves: Cross-Correlations of Lensed Primary CMB B-Modes with Large-Scale Structure.

We propose a new probe of inflationary gravitational waves (IGWs): the cross-correlation of the lensing of inflationary B-mode polarization with a large-scale structure (LSS) tracer, which can also be a cosmic microwave background (CMB) lensing map. This is equivalent to measuring a three-point function of two CMB B-modes and an LSS tracer. We forecast expected 1σ constraints on the tensor-to-scalar ratio r, albeit with a simplistic foreground treatment, and find constraints of σ_{r}≃7×10^{-3} from the correlation of CMB-S4-Deep B-mode lensing and LSST galaxies, σ_{r}≃5×10^{-3} from the correlation of CMB-S4-Deep B-mode lensing and CMB-S4-Deep CMB lensing, and σ_{r}≃10^{-2} from the correlation of LiteBIRD B-mode lensing and CMB-S4-Wide lensing. Because this probe is inherently non-Gaussian, simple Gaussian foregrounds will not produce any biases to the measurement of r. While a detailed investigation of non-Gaussian foreground contamination for different cross-correlations will be essential, this observable has the potential to be a useful probe of IGWs, which, due to different sensitivity to many potential sources of systematic errors, can be complementary to standard methods for constraining r.