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The tightest constraints on the tensor-to-scalar ratiorcan only be obtained after removing a substantial fraction of the lensingB-mode sample variance. The planned Cosmic Microwave Background (CMB)-S4 experiment (cmb-s4.org) will remove the lensingB-mode signal internally by reconstructing the gravitational lenses from high-resolution observations. We document here a first lensing reconstruction pipeline able to achieve this optimally for arbitrary sky coverage. We make it part of a map-based framework to test CMB-S4 delensing performance and its constraining power onr, including inhomogeneous noise and two non-Gaussian Galactic polarized foreground models. The framework performs component separation of the high-resolution maps, followed by the construction of lensingB-mode templates, which are then included in a parametric small-aperture map cross-spectra-based likelihood forr. We find that the lensing reconstruction and framework achieve the expected performance, compatible with the targetσ(r) ≃ 5 · 10⁻⁴in the absence of a tensor signal, after an effective removal of 92%–93% of the lensingB-mode variance, depending on the simulation set. The code for the lensing reconstruction can also be used for cross-correlation studies with large-scale structures, lensing spectrum reconstruction, cluster lensing, or other CMB lensing-related purposes. As part of our tests, we also demonstrate the joint optimal reconstruction of the lensing potential with the lensing curl potential mode at second order in the density fluctuations.

 

We present new measurements of cosmic microwave background (CMB) lensing over 9400 deg²of the sky. These lensing measurements are derived from the Atacama Cosmology Telescope (ACT) Data Release 6 (DR6) CMB data set, which consists of five seasons of ACT CMB temperature and polarization observations. We determine the amplitude of the CMB lensing power spectrum at 2.3% precision (43σsignificance) using a novel pipeline that minimizes sensitivity to foregrounds and to noise properties. To ensure that our results are robust, we analyze an extensive set of null tests, consistency tests, and systematic error estimates and employ a blinded analysis framework. Our CMB lensing power spectrum measurement provides constraints on the amplitude of cosmic structure that do not depend on Planck or galaxy survey data, thus giving independent information about large-scale structure growth and potential tensions in structure measurements. The baseline spectrum is well fit by a lensing amplitude ofA_lens= 1.013 ± 0.023 relative to the Planck 2018 CMB power spectra best-fit ΛCDM model andA_lens= 1.005 ± 0.023 relative to the ACT DR4 + WMAP best-fit model. From our lensing power spectrum measurement, we derive constraints on the parameter combination$S_8^{\mathrm{CMBL}}\equiv {\sigma }_8{\left({\mathrm{\Omega }}_m/0.3\right)}^{0.25}$of$S_8^{\mathrm{CMBL}}=0.818\pm 0.022$from ACT DR6 CMB lensing alone and$S_8^{\mathrm{CMBL}}=0.813\pm 0.018$when combining ACT DR6 and PlanckNPIPECMB lensing power spectra. These results are in excellent agreement with ΛCDM model constraints from Planck or ACT DR4 + WMAP CMB power spectrum measurements. Our lensing measurements from redshiftsz∼ 0.5–5 are thus fully consistent with ΛCDM structure growth predictions based on CMB anisotropies probing primarilyz∼ 1100. We find no evidence for a suppression of the amplitude of cosmic structure at low redshifts.

 

Abstract CMB-S4—the next-generation ground-based cosmic microwave background (CMB) experiment—is set to significantly advance the sensitivity of CMB measurements and enhance our understanding of the origin and evolution of the universe. Among the science cases pursued with CMB-S4, the quest for detecting primordial gravitational waves is a central driver of the experimental design. This work details the development of a forecasting framework that includes a power-spectrum-based semianalytic projection tool, targeted explicitly toward optimizing constraints on the tensor-to-scalar ratio, r , in the presence of Galactic foregrounds and gravitational lensing of the CMB. This framework is unique in its direct use of information from the achieved performance of current Stage 2–3 CMB experiments to robustly forecast the science reach of upcoming CMB-polarization endeavors. The methodology allows for rapid iteration over experimental configurations and offers a flexible way to optimize the design of future experiments, given a desired scientific goal. To form a closed-loop process, we couple this semianalytic tool with map-based validation studies, which allow for the injection of additional complexity and verification of our forecasts with several independent analysis methods. We document multiple rounds of forecasts for CMB-S4 using this process and the resulting establishment of the current reference design of the primordial gravitational-wave component of the Stage-4 experiment, optimized to achieve our science goals of detecting primordial gravitational waves for r > 0.003 at greater than 5 σ , or in the absence of a detection, of reaching an upper limit of r < 0.001 at 95% CL.