Reaching σ(r) ≈ 10⁻³ with CMB B-modes: delensing efficiency and Galactic foreground residuals

BICEP/Keck through the 2018 season gives r < 0.036 at 95% CL, and r < 0.032 combined with Planck and BAO (arXiv:2110.00483; Tristram et al., arXiv:2112.07961). Delensing was proposed with external datasets (Smith, Hanson & LoVerde, arXiv:1010.0048) and was demonstrated on BICEP/Keck data with a lensing B-mode template built from SPT, BICEP/Keck and Planck polarisation and the Planck CIB map (arXiv:2011.08163). Planck dust polarisation power spectra (arXiv:1409.5738) found a dust BB/EE amplitude ratio of about 0.5, no dust-free windows anywhere on the sky, and a dust BB power in the BICEP2 field comparable to the BICEP2 signal itself. The Simons Observatory forecasts σ(r) ≈ 0.002–0.003 with its small-aperture telescopes (arXiv:1808.07445). In July 2025 DOE and NSF jointly decided they could no longer support the CMB-S4 project (statement reproduced on the project site and reported by Science), removing the planned σ(r) ≈ 5×10⁻⁴ ground experiment. The best limit is still essentially BK18: a December 2025 combination of the latest CMB and BAO data gives r < 0.034 (Balkenhol et al., arXiv:2512.10613), and SPT-3G alone reaches r < 0.25 (arXiv:2505.02827). BICEP Array and the Simons Observatory small-aperture telescopes have not yet published r constraints; LiteBIRD (planned for the early 2030s) targets σ(r) ≲ 10⁻³. No detection of primordial B-modes has been claimed.

A detection at r ≈ 0.01 would establish the energy scale of inflation (about 10¹⁶ GeV), the quantum nature of gravity via the tensor spectrum and select classes of inflation models. Delensing and component separation methods are reused in cosmic-shear and intensity-mapping work. No practical application.

Resolved by a detection of primordial B-modes at ≥5σ with demonstrated foreground-residual robustness across frequency and sky patches, or by an upper limit r < 0.003 at 95% CL with total systematic bias ≤10⁻³.