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Atacama Cosmology Telescope: B-mode delensing with DR6 data and external tracers of large-scale structure

Emilie Hertig1,2,*, Antón Baleato Lizancos3,4,5, Frank J. Qu6,7, J. Richard Bond8, Erminia Calabrese9, Anthony Challinor1,2,10, Mark J. Devlin11, Jo Dunkley12,13, Thibaut Louis14 et al. (ACT Collaboration)

Thibaut Louis14, Mathew S. Madhavacheril11, Toshiya Namikawa9,15,2, Lyman A. Page12, Neelima Sehgal16, Blake Sherwin10,2, Cristóbal Sifón17, Suzanne T. Staggs12, and Edward J. Wollack18 (ACT Collaboration)

  • *Contact author: emh83@cam.ac.uk
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Phys. Rev. D 113, 123530 – Published 15 June, 2026

DOI: https://doi.org/10.1103/ztry-pnlx

Abstract

Large-scale B-mode polarization of the cosmic microwave background (CMB) is a prime target for current and future experiments in search of primordial gravitational waves. With increasingly sensitive instruments being deployed, secondary B-modes induced by the weak gravitational lensing of CMB photons are becoming an important limitation and need to be removed, a process known as delensing. In this work, we combine internally reconstructed CMB lensing maps from the Atacama Cosmology Telescope (ACT) data release 6 (DR6) with galaxy samples from unWISE and a map of the cosmic infrared background (CIB) fluctuations from Planck to produce a well-correlated tracer of the CMB lensing field. Our coadded tracer, shown to be 55%–85% correlated with the true lensing convergence at multipoles L≤2000, is then convolved with ACT DR6 E-mode polarization to yield a template of the lensing B-modes. We assess its performance on a wide range of scales by using it to delens ACT DR6 and Planck B-modes over 23% of the sky, removing around 39% of the lensing power at 100≤l≤1500 and 47% at 30≤l≤300, respectively. Our template achieves the highest delensing efficiency to date and will be useful for the analysis of early polarization maps from the Simons Observatory. We finally outline prospects for further improvements by including additional large-scale structure tracers from upcoming cosmological surveys.

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References (112)

  1. Planck Collaboration, Planck 2018 results: VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020).
  2. E. Calabrese et al., The Atacama Cosmology Telescope: DR6 constraints on extended cosmological models, J. Cosmol. Astropart. Phys. 11 (2025) 063.
  3. E. Camphuis et al., SPT-3G D1: CMB temperature and polarization power spectra and cosmology from 2019 and 2020 observations of the SPT-3G Main field, Phys. Rev. D 113, 083504 (2026).
  4. R. Brout, F. Englert, and E. Gunzig, The creation of the universe as a quantum phenomenon, Ann. Phys. 115, 78 (1978).
  5. A. A. Starobinsky, A new type of isotropic cosmological models without singularity, Phys. Lett. 91B, 99 (1980).
  6. D. Kazanas, Dynamics of the universe and spontaneous symmetry breaking, Astrophys. J. Lett. 241, L59 (1980).
  7. K. Sato, First-order phase transition of a vacuum and the expansion of the universe, Mon. Not. R. Astron. Soc. 195, 467 (1981).
  8. A. H. Guth, Inflationary universe: A possible solution to the horizon and flatness problems, Phys. Rev. D 23, 347 (1981).
  9. A. Albrecht and P. J. Steinhardt, Cosmology for grand unified theories with radiatively induced symmetry breaking, Phys. Rev. Lett. 48, 1220 (1982).
  10. A. D. Linde, A new inflationary universe scenario: A possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems, Phys. Lett. 108B, 389 (1982).
  11. A. D. Linde, Chaotic inflation, Phys. Lett. 129B, 177 (1983).
  12. A. A. Starobinsky, Spectrum of relict gravitational radiation and the early state of the universe, Sov. J. Exp. Theor. Phys. Lett. 30, 682 (1979).
  13. V. F. Mukhanov and G. V. Chibisov, Quantum fluctuations and a nonsingular universe, Sov. J. Exp. Theor. Phys. Lett. 33, 532 (1981).
  14. L. F. Abbott and M. B. Wise, Constraints on generalized inflationary cosmologies, Nucl. Phys. B244, 541 (1984).
  15. M. Zaldarriaga and U. Seljak, All-sky analysis of polarization in the microwave background, Phys. Rev. D 55, 1830 (1997).
  16. M. Kamionkowski, A. Kosowsky, and A. Stebbins, Statistics of cosmic microwave background polarization, Phys. Rev. D 55, 7368 (1997).
  17. U. Seljak and M. Zaldarriaga, Signature of gravity waves in the polarization of the microwave background, Phys. Rev. Lett. 78, 2054 (1997).
  18. M. Kamionkowski, A. Kosowsky, and A. Stebbins, A probe of primordial gravity waves and vorticity, Phys. Rev. Lett. 78, 2058 (1997).
  19. G. Hinshaw et al., Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological parameter results, Astrophys. J. Suppl. Ser. 208, 19 (2013).
  20. Planck Collaboration, Planck 2018 results. X. Constraints on inflation, Astron. Astrophys. 641, A10 (2020).
  21. BICEP/Keck Collaboration, BICEP/Keck XIII: Improved constraints on primordial gravitational waves using Planck, WMAP, and BICEP/Keck observations through the 2018 observing season, Phys. Rev. Lett. 127, 151301 (2021).
  22. M. Tristram et al., Improved limits on the tensor-to-scalar ratio using BICEP and Planck, Phys. Rev. D 105, 083524 (2022).
  23. F. L. Bezrukov and M. E. Shaposhnikov, The standard model Higgs boson as the inflaton, Phys. Lett. B 659, 703 (2008).
  24. The Simons Observatory Collaboration, The Simons Observatory: Science goals and forecasts, J. Cosmol. Astropart. Phys. 02 (2019) 056.
  25. CMB-S4 Project and Collaboration, Revised CMB-S4 Project Plan, Technical Report, 2025.
  26. LiteBIRD Collaboration, Probing cosmic inflation with the LiteBIRD cosmic microwave background polarization survey, Prog. Theor. Exp. Phys. 2023, 042F01 (2023).
  27. N. Katayama and E. Komatsu, Simple foreground cleaning algorithm for detecting primordial B-mode polarization of the cosmic microwave background, Astrophys. J. 737, 78 (2011).
  28. B. Thorne et al., Removal of galactic foregrounds for the Simons Observatory primordial gravitational wave search, arXiv:1905.08888.
  29. J. Chluba, J. C. Hill, and M. H. Abitbol, Rethinking CMB foregrounds: Systematic extension of foreground parameterizations, Mon. Not. R. Astron. Soc. 472, 1195 (2017).
  30. M. Zaldarriaga and U. Seljak, Gravitational lensing effect on cosmic microwave background polarization, Phys. Rev. D 58, 023003 (1998).
  31. A. Lewis and A. Challinor, Weak gravitational lensing of the CMB, Phys. Rep. 429, 1 (2006).
  32. D. Hanson et al., Detection of B-mode polarization in the cosmic microwave background with data from the South Pole Telescope, Phys. Rev. Lett. 111, 141301 (2013).
  33. T. Namikawa et al., The Simons Observatory: Constraining inflationary gravitational waves with multi-tracer B-mode delensing, Phys. Rev. D 105, 023511 (2022).
  34. J. Carron, A. Lewis, and A. Challinor, Internal delensing of Planck CMB temperature and polarization, J. Cosmol. Astropart. Phys. 05 (2017) 035.
  35. Planck Collaboration, Planck 2018 results: VIII. Gravitational lensing, Astron. Astrophys. 641, A8 (2020).
  36. D. Han et al., The Atacama Cosmology Telescope: Delensed power spectra and parameters, J. Cosmol. Astropart. Phys. 01 (2021) 031.
  37. BICEP/Keck and SPTpol Collaborations, A demonstration of improved constraints on primordial gravitational waves with delensing, Phys. Rev. D 103, 022004 (2021).
  38. A. Manzotti et al., CMB polarization B-mode delensing with SPTpol and Herschel, Astrophys. J. 846, 45 (2017).
  39. A. Baleato Lizancos, A. Challinor, and J. Carron, Limitations of CMB B-mode template delensing, Phys. Rev. D 103, 023518 (2021).
  40. F. J. Qu et al., The Atacama Cosmology Telescope: A measurement of the DR6 CMB lensing power spectrum and its implications for structure growth, Astrophys. J. 962, 112 (2024).
  41. S. Adachi et al., Internal delensing of cosmic microwave background polarization B-modes with the POLARBEAR experiment, Phys. Rev. Lett. 124, 131301 (2020).
  42. J. Carron and A. Lewis, Maximum a posteriori CMB lensing reconstruction, Phys. Rev. D 96, 063510 (2017).
  43. S. Belkner et al., CMB-S4: Iterative internal delensing and r constraints, Astrophys. J. 964, 148 (2024).
  44. B. D. Sherwin and M. Schmittfull, Delensing the CMB with the cosmic infrared background, Phys. Rev. D 92, 043005 (2015).
  45. P. Larsen et al., Demonstration of cosmic microwave background delensing using the cosmic infrared background, Phys. Rev. Lett. 117, 151102 (2016).
  46. B. Yu, J. C. Hill, and B. D. Sherwin, Multitracer CMB delensing maps from Planck and WISE data, Phys. Rev. D 96, 123511 (2017).
  47. E. F. Schlafly et al., The unWISE catalog: Two billion infrared sources from five years of WISE imaging, Astrophys. J. Suppl. Ser. 240, 30 (2019).
  48. A. Challinor and G. Chon, Geometry of weak lensing of CMB polarization, Phys. Rev. D 66, 127301 (2002).
  49. T. Okamoto and W. Hu, CMB lensing reconstruction on the full sky, Phys. Rev. D 67, 083002 (2003).
  50. J. N. Goldberg et al., Spin-s spherical harmonics and ð, J. Math. Phys. (N.Y.) 8, 2155 (1967).
  51. A. Lewis, A. Challinor, and N. Turok, Analysis of CMB polarization on an incomplete sky, Phys. Rev. D 65, 023505 (2002).
  52. A. S. Maniyar et al., Quadratic estimators for CMB weak lensing, Phys. Rev. D 103, 083524 (2021).
  53. Z. Gao, Z. Vlah, and A. Challinor, Flat-sky angular power spectra revisited, J. Cosmol. Astropart. Phys. 02 (2024) 003.
  54. S. Wang, A. Baleato Lizancos, and J. L. Bernal, Delensing CMB B-modes using galaxy surveys: The effect of galaxy bias and matter clustering non-linearities, Phys. Rev. D 112, 123535 (2025).
  55. N. R. Hall et al., Angular power spectra of the millimeter wavelength background light from dusty star-forming galaxies with the South Pole Telescope, Astrophys. J. 718, 632 (2010).
  56. D. N. Limber, The analysis of counts of the extragalactic nebulae in terms of a fluctuating density field., Astrophys. J. 117, 134 (1953).
  57. T. Namikawa et al., LiteBIRD science goals and forecasts: Improving sensitivity to inflationary gravitational waves with multitracer delensing, J. Cosmol. Astropart. Phys. 06 (2024) 010.
  58. H. K. Eriksen et al., Power spectrum estimation from high-resolution maps by Gibbs sampling, Astrophys. J. Suppl. Ser. 155, 227 (2004).
  59. E. Hertig et al., The Simons Observatory: Combining cross-spectral foreground cleaning with multitracer B-mode delensing for improved constraints on inflation, Phys. Rev. D 110, 043532 (2024).
  60. ACT DR6 Lensing Maps, https://lambda.gsfc.nasa.gov/product/act/actadv_dr6_lensing_maps_get.html (accessed: 2026-04-23).
  61. M. Madhavacheril et al., The Atacama Cosmology Telescope: DR6 gravitational lensing map and cosmological parameters, Astrophys. J. 962, 113 (2024).
  62. S. K. Choi et al., The Atacama Cosmology Telescope: A measurement of the cosmic microwave background power spectra at 98 and 150 GHz, J. Cosmol. Astropart. Phys. 12 (2020) 045.
  63. N. MacCrann et al., The Atacama Cosmology Telescope: Mitigating the impact of extragalactic foregrounds for the DR6 CMB lensing analysis, Astrophys. J. 966, 138 (2024).
  64. A. Baleato Lizancos and S. Ferraro, The impact of extragalactic foregrounds on internal delensing of CMB B-mode polarization, Phys. Rev. D 106, 063534 (2022).
  65. A. Baleato Lizancos, W. Coulton, A. Challinor, B. D. Sherwin, and Y. Mehta, A halo model of extragalactic contamination to CMB lensing, delensing, and cross-correlations, J. Cosmol. Astropart. Phys. 11 (2025) 031.
  66. M. S. Madhavacheril, K. M. Smith, B. D. Sherwin, and S. Naess, CMB lensing power spectrum estimation without instrument noise bias, J. Cosmol. Astropart. Phys. 05 (2021) 028.
  67. A. Krolewski et al., unWISE tomography of Planck CMB lensing, J. Cosmol. Astropart. Phys. 05 (2020) 047.
  68. unWISE Galaxy Catalog, https://catalog.unwise.me/catalogs.html (accessed: 2026-04-23).
  69. E. L. Wright et al., The wide-field infrared survey explorer (WISE): Mission description and initial on-orbit performance, Astron. J. 140, 1868 (2010).
  70. A. Mainzer et al., Initial performance of the NEOWISE reactivation mission, Astrophys. J. 792, 30 (2014).
  71. C. Laigle et al., The COSMOS2015 catalog: Exploring the 1<z<6 Universe with half a million galaxies, Astrophys. J. Suppl. Ser. 224, 24 (2016).
  72. G. S. Farren et al., The Atacama Cosmology Telescope: Cosmology from cross-correlations of unWISE galaxies and ACT DR6 CMB lensing, Astrophys. J. 966, 157 (2024).
  73. K. M. Górski et al., healpix: A framework for high-resolution discretization and fast analysis of data distributed on the sphere, Astrophys. J. 622, 759 (2005).
  74. Planck Collaboration, Planck intermediate results. XLVIII. Disentangling Galactic dust emission and cosmic infrared background anisotropies, Astron. Astrophys. 596, A109 (2016).
  75. M. Remazeilles, J. Delabrouille, and J.-F. Cardoso, Foreground component separation with generalised ILC, Mon. Not. R. Astron. Soc. 418, 467 (2011).
  76. F. McCarthy, Large-scale galactic-dust-cleaned cosmic infrared background maps from Planck PR4 and HI4PI with pyilc, arXiv:2405.13470.
  77. A. Lewis, A. Challinor, and A. Lasenby, Efficient computation of CMB anisotropies in closed FRW models, Astrophys. J. 538, 473 (2000).
  78. E. Calabrese et al., Cosmological parameters from pre-Planck CMB measurements: A 2017 update, Phys. Rev. D 95, 063525 (2017).
  79. S. Naess, M. Madhavacheril, and M. Hasselfield, Pixell: Rectangular pixel map manipulation and harmonic analysis library, https://ascl.net/2102.003 (2021), Astrophysics Source Code Library ascl:2102.003.
  80. Z. Atkins et al., The Atacama Cosmology Telescope: Map-based noise simulations for DR6, J. Cosmol. Astropart. Phys. 11 (2023) 073.
  81. N. Sehgal et al., Simulations of the microwave sky, Astrophys. J. 709, 920 (2010).
  82. G. Stein et al., The Websky extragalactic CMB simulations, J. Cosmol. Astropart. Phys. 10 (2020) 012.
  83. T. Namikawa and R. Takahashi, Impact of nonlinear growth of the large-scale structure on CMB B-mode delensing, Phys. Rev. D 99, 023530 (2019).
  84. A. Baleato Lizancos et al., Delensing the CMB with the cosmic infrared background: The impact of foregrounds, Mon. Not. R. Astron. Soc. 514, 5786 (2022).
  85. D. Alonso, J. Sanchez, and A. Slosar, A unified pseudo-Cℓ framework, Mon. Not. R. Astron. Soc. 484, 4127 (2019).
  86. E. Hivon et al., MASTER of the CMB anisotropy power spectrum: A fast method for statistical analysis of large and complex CMB data sets, Astrophys. J. 567, 2 (2002).
  87. L. Knox, Determination of inflationary observables by cosmic microwave background anisotropy experiments, Phys. Rev. D 52, 4307 (1995).
  88. K. M. Smith, Pseudo-Cℓ estimators which do not mix E and B modes, Phys. Rev. D 74, 083002 (2006).
  89. A. MacInnis, N. Sehgal, and M. Rothermel, Cosmological parameter forecasts for a CMB-HD survey, Phys. Rev. D 109, 063527 (2024).
  90. N. Sehgal et al., Internal delensing of cosmic microwave background acoustic peaks, Phys. Rev. D 95, 103512 (2017).
  91. A. Baleato Lizancos, A. Challinor, and J. Carron, Impact of internal-delensing biases on searches for primordial B-modes of CMB polarisation, J. Cosmol. Astropart. Phys. 03 (2021) 016.
  92. Planck Legacy Archive, https://pla.esac.esa.int/#maps (accessed: 2026-04-23).
  93. Planck Collaboration, Planck 2018 results. IV. Diffuse component separation, Astron. Astrophys. 641, A4 (2020).
  94. J. A. Sobrin et al., The design and integrated performance of SPT-3G, Astrophys. J. Suppl. Ser. 258, 42 (2022).
  95. Z. Ivezić et al., LSST: From science drivers to reference design and anticipated data products, Astrophys. J. 873, 111 (2018).
  96. A. Baleato Lizancos and M. White, The impact of anisotropic redshift distributions on angular clustering, J. Cosmol. Astropart. Phys. 07 (2023) 044.
  97. D. Beck, J. Errard, and R. Stompor, Impact of polarized galactic foreground emission on CMB lensing reconstruction and delensing of B-modes, J. Cosmol. Astropart. Phys. 06 (2020) 030.
  98. A. J. Ross et al., The construction of large-scale structure catalogs for the dark energy spectroscopic instrument, J. Cosmol. Astropart. Phys. 01 (2025) 125.
  99. S. Ilić et al., Euclid preparation—XV. Forecasting cosmological constraints for the Euclid and CMB joint analysis, Astron. Astrophys. 657, A91 (2022).
  100. LSST Science Collaboration, LSST Science Book, Version 2.0, arXiv:0912.0201.
  101. A. Baleato Lizancos and M. White, Harmonic analysis of discrete tracers of large-scale structure, J. Cosmol. Astropart. Phys. 05 (2024) 010.
  102. K. N. Abazajian et al., CMB-S4 science book, first edition, arXiv:1610.02743.
  103. A. Zonca et al., healpy: Equal area pixelization and spherical harmonics transforms for data on the sphere in Python, J. Open Source Software 4, 1298 (2019).
  104. T. Namikawa, cmblensplus: A tool to analyze cosmic microwave background anisotropies, Astrophysics Source Code Library, record ascl:2104.021 (2021).
  105. C. R. Harris et al., Array programming with numpy, Nature (London) 585, 357 (2020).
  106. P. Virtanen et al., scipy1.0: Fundamental algorithms for scientific computing in Python, Nat. Methods 17, 261 (2020).
  107. J. D. Hunter, matplotlib: A 2D graphics environment, Comput. Sci. Eng. 9, 90 (2007).
  108. A. Dey et al., Overview of the DESI legacy imaging surveys, Astron. J. 157, 168 (2019).
  109. R. Zhou et al., DESI luminous red galaxy samples for cross-correlations, J. Cosmol. Astropart. Phys. 11 (2023) 097.
  110. R. Zhou et al., Target selection and validation of DESI luminous red galaxies, Astron. J. 165, 58 (2023).
  111. E. Rosenberg, S. Gratton, and A. Challinor, Filtering in CMB data analysis with application to ACT DR4 and Planck, Phys. Rev. D 112, 023534 (2025).
  112. T. Namikawa, CMB internal delensing with general optimal estimator for higher-order correlations, Phys. Rev. D 95, 103514 (2017).

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Phys. Rev. D 113, 123530– Published 15 June, 2026
  • Received 3 December 2025
  • Accepted 17 April 2026
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