Delensing for Precision Cosmology: Optimizing Future CMB B-mode Surveys to Constrain r

The detection of primordial B-modes, a key probe of cosmic inflation, is increasingly challenged by contamination from weak gravitational lensing B-modes induced by large-scale structure (LSS). We present a delensing pipeline designed to enhance the sensitivity to the inflationary parameter r, minimizing reliance on foreground mitigation during lensing reconstruction. Using simulations of Simons Observatory-like CMB observations and Euclid-like LSS surveys in the Northern hemisphere, we demonstrate that excluding low-l modes (l<200) effectively mitigates foreground biases, enabling robust lensing potential reconstruction using observed CMB polarization maps. We reconstruct the lensing potential with a minimum-variance (MV) quadratic estimator (QE) applied to CMB polarization data and combine this with external LSS tracers to improve delensing efficiency. Two complementary methods, the Gradient-order template and the Inverse-lensing approach, are used to generate lensing B-mode templates, which are cross-correlated with observed B-modes. This achieves a 40 percent reduction in the uncertainty of r with CMB-only reconstruction, improving to 60 percent when incorporating external LSS tracers. We validate our results using both the Hamimeche and Lewis likelihood and a Gaussian approximation, finding consistent constraints on r. Our work establishes a streamlined framework for ground-based CMB experiments, demonstrating that synergies with LSS surveys significantly enhance sensitivity to primordial gravitational waves.