Impact of post-Born lensing on the CMB

Lensing of the CMB is affected by post-Born lensing, producing corrections to the convergence power spectrum and introducing field rotation. We show numerically that the lensing convergence power spectrum is affected at the $\lesssim 0.2\%$ level on accessible scales, and that this correction and the field rotation are negligible for observations with arcminute beam and noise levels $\gtrsim 1 \mu {\text{K}}\,{\text{arcmin}} $. The field rotation generates $\sim 2.5\%$ of the total lensing B-mode polarization amplitude ($0.2\%$ in power on small scales), but has a blue spectrum on large scales, making it highly subdominant to the convergence B modes on scales where they are a source of confusion for the signal from primordial gravitational waves. Since the post-Born signal is non-linear, it also generates a bispectrum with the convergence. We show that the post-Born contributions to the bispectrum substantially change the shape predicted from large-scale structure non-linearities alone, and hence must be included to estimate the expected total signal and impact of bispectrum biases on CMB lensing reconstruction quadratic estimators and other observables. The field-rotation power spectrum only becomes potentially detectable for noise levels $\ll 1 \mu {\text{K}}\,{\text{arcmin}}$, but its bispectrum with the convergence may be observable at $\sim 3\sigma$ with Stage IV observations. Rotation-induced and convergence-induced B modes are slightly correlated by the bispectrum, and the bispectrum also produces additional contributions to the lensed BB power spectrum.