Impact of nonlinear growth of the large-scale structure on CMB B-mode delensing

We study the impact of the nonlinear growth of the large-scale structure (LSS) on the removal of the gravitational lensing effect (delensing) in cosmic microwave background (CMB) $B$ modes. The importance of the nonlinear growth of the LSS in the gravitational lensing analysis of CMB has been recently recognized by several works, while its impact on delensing is not yet explored. The delensing using mass-tracers such as galaxies and cosmic infrared background (CIB) could be also affected by the nonlinear growth. We find that the nonlinear growth of the LSS leads to $\sim 0.3\%$ corrections to $B$-mode spectrum after delensing with a high-$z$ mass tracer ($z_m\sim 2$) at $\ell=1000$-$2000$. The off-diagonal correlation coefficients of the lensing $B$-mode template spectrum become significant for delensing with low-$z$ tracers ($z_m\lesssim 0.5$), but are negligible with high-$z$ tracers (such as CIB). On the other hand, the power spectrum covariance of the delensed $B$ mode is not significantly affected by the nonlinear growth of the LSS, and the delensing efficiency is not significantly changed even if we use low-$z$ tracers. The CMB $B$-mode internal delensing is also not significantly affected by the nonlinear growth.