We present a constraint on the tensor-to-scalar ratio, r, derived from measurements of cosmic microwave background (CMB) polarization B-modes with "delensing,"whereby the uncertainty on r contributed by the sample variance of the gravitational lensing B-modes is reduced by cross-correlating against a lensing B-mode template. This template is constructed by combining an estimate of the polarized CMB with a tracer of the projected large-scale structure. The large-scale-structure tracer used is a map of the cosmic infrared background derived from Planck satellite data, while the polarized CMB map comes from a combination of South Pole Telescope, bicep/Keck, and Planck data. We expand the bicep/Keck likelihood analysis framework to accept a lensing template and apply it to the bicep/Keck dataset collected through 2014 using the same parametric foreground modeling as in the previous analysis. From simulations, we find that the uncertainty on r is reduced by ∼10%, from σ(r)=0.024 to 0.022, which can be compared with a ∼26% reduction obtained when using a perfect lensing template or if there were zero lensing B-modes. Applying the technique to the real data, the constraint on r is improved from r0.05<0.090 to r0.05<0.082 (95% C.L.). This is the first demonstration of improvement in an r constraint through delensing.
Bibliographical noteFunding Information:
The authors thank Dominic Beck and Chang Feng for useful comments on an early version of the draft. The bicep 2/Keck Array projects have been made possible through a series of grants from the National Science Foundation including Grants No. 0742818, No. 0742592, No. 1044978, No. 1110087, No. 1145172, No. 1145143, No. 1145248, No. 1639040, No. 1638957, No. 1638978, and No. 1638970, and by the Keck Foundation. The development of antenna-coupled detector technology was supported by the JPL Research and Technology Development Fund, and by NASA Grants No. 06-ARPA206-0040, No. 10-SAT10-0017, No. 12-SAT12-0031, No. 14-SAT14-0009, and No. 16-SAT-16-0002. The development and testing of focal planes were supported by the Gordon and Betty Moore Foundation at Caltech. Readout electronics were supported by a Canada Foundation for Innovation grant to UBC. Support for quasioptical filtering was provided by UK STFC Grant No. ST/N000706/1. Some of the computations in this paper were run on the Odyssey cluster supported by the FAS Science Division Research Computing Group at Harvard University. The analysis effort at Stanford and S. L. A. C. is partially supported by the U.S. DOE Office of Science. We thank the staff of the U.S. Antarctic Program and in particular the South Pole Station without whose help this research would not have been possible. Most special thanks go to our heroic winter-overs Robert Schwarz and Steffen Richter. We thank all those who have contributed past efforts to the bicep –Keck Array series of experiments, including the bicep 1 team. S. P. T. is supported by the National Science Foundation through Grants No. PLR-1248097 and No. OPP-1852617. Partial support is also provided by the NSF Physics Frontier Center Grant No. PHY-1125897 to the Kavli Institute of Cosmological Physics at the University of Chicago, the Kavli Foundation and the Gordon and Betty Moore Foundation Grant No. GBMF 947. This research used resources of the National Energy Research Scientific Computing Center (NERSC), a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. The Melbourne group acknowledges support from the University of Melbourne and an Australian Research Council’s Future Fellowship (FT150100074). Work at Argonne National Lab is supported by UChicago Argonne LLC, Operator of Argonne National Laboratory (Argonne). Argonne, a U.S. Department of Energy Office of Science Laboratory, is operated under Contract No. DE-AC02-06CH11357. We also acknowledge support from the Argonne Center for Nanoscale Materials. Work at McGill is supported by the Natural Science and Engineering Research Council of Canada, the Canadian Institute for Advanced Research, and M. D. acknowledges a Killam research fellowship W. L. K. W. is supported in part by the Kavli Institute for Cosmological Physics at the University of Chicago through Grant No. NSF PHY-1125897, an endowment from the Kavli Foundation and its founder Fred Kavli, and by the Department of Energy, Laboratory Directed Research and Development program and as part of the Panofsky Fellowship program at SLAC National Accelerator Laboratory, under Contract No. DE-AC02-76SF00515. B. B. is supported by the Fermi Research Alliance LLC under Contract No. De-AC02- 07CH11359 with the U.S. Department of Energy. We acknowledge the use of many p ython packages: ip ython , m atplotlib , s ci p y , and healpy . We also thank the Planck and WMAP teams for the use of their data. Some of the sky simulations used in this paper were developed by the WebSky Extragalactic CMB Mocks team, with the continuous support of the Canadian Institute for Theoretical Astrophysics (CITA), the Canadian Institute for Advanced Research (CIFAR), and the Natural Sciences and Engineering Research Council of Canada (NSERC), and were generated on the Niagara supercomputer at the SciNet HPC Consortium. SciNet is funded by: the Canada Foundation for Innovation under the auspices of Compute Canada; the Government of Ontario; Ontario Research Fund—Research Excellence; and the University of Toronto.
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