Search

Motivated by observed discrepancies between ACT DR4 and Planck 2018 cosmic microwave background (CMB) anisotropy power spectra, particularly in the cross-correlation of temperature and E-mode polarization, we investigate challenges that may be encountered in the comparison of satellite and ground-based CMB data. In particular, we focus on the effects of Fourier-space filtering and masking involving bright point sources. We show that the filtering operation generates bright cross-shaped artifacts in the map, which stretch far outside typical point-source masks. If not corrected, these artifacts can add bias or additional variance to cross-spectra, skewing results. However we find that the effect of this systematic is not large enough to explain the ACT-Planck differences presented with ACT DR4., Comment: 15 pages, 8 figures

The Simons Observatory (SO), a next-generation ground-based CMB experiment in its final stages of construction, will target primordial $B$-modes with unprecedented sensitivity to set tight bounds on the amplitude of inflationary gravitational waves. Aiming to infer the tensor-to-scalar ratio $r$ with precision $\sigma(r=0) \leq 0.003$, SO will rely on powerful component-separation algorithms to distinguish the faint primordial signal from stronger sources of large-scale $B$-modes such as Galactic foregrounds and weak gravitational lensing. We present an analysis pipeline that performs delensing and foreground cleaning simultaneously by including multifrequency CMB data and a lensing $B$-mode template in a power-spectrum-based likelihood. Here, we demonstrate this algorithm on masked SO-like simulations containing inhomogeneous noise and non-Gaussian foregrounds. The lensing convergence is reconstructed from high-resolution simulations of the CMB and external mass tracers. Using optimized pixel weights for power spectrum estimation, the target precision for SO's nominal design is achieved and delensing reduces $\sigma(r)$ by 27-37%, depending on foreground complexity., Comment: 4 pages, 4 figures. Contribution to the 2024 Cosmology session of the 58th Rencontres de Moriond

The Simons Observatory (SO), due to start full science operations in early 2025, aims to set tight constraints on inflationary physics by inferring the tensor-to-scalar ratio $r$ from measurements of CMB polarization $B$-modes. Its nominal design targets a precision $\sigma(r=0) \leq 0.003$ without delensing. Achieving this goal and further reducing uncertainties requires the mitigation of other sources of large-scale $B$-modes such as Galactic foregrounds and weak gravitational lensing. We present an analysis pipeline aiming to estimate $r$ by including delensing within a cross-spectral likelihood, and demonstrate it on SO-like simulations. Lensing $B$-modes are synthesised using internal CMB lensing reconstructions as well as Planck-like CIB maps and LSST-like galaxy density maps. This $B$-mode template is then introduced into SO's power-spectrum-based foreground-cleaning algorithm by extending the likelihood function to include all auto- and cross-spectra between the lensing template and the SAT $B$-modes. Within this framework, we demonstrate the equivalence of map-based and cross-spectral delensing and use it to motivate an optimized pixel-weighting scheme for power spectrum estimation. We start by validating our pipeline in the simplistic case of uniform foreground spectral energy distributions (SEDs). In the absence of primordial $B$-modes, $\sigma(r)$ decreases by 37% as a result of delensing. Tensor modes at the level of $r=0.01$ are successfully detected by our pipeline. Even with more realistic foreground models including spatial variations in the dust and synchrotron spectral properties, we obtain unbiased estimates of $r$ by employing the moment-expansion method. In this case, delensing-related improvements range between 27% and 31%. These results constitute the first realistic assessment of the delensing performance at SO's nominal sensitivity level. (Abridged), Comment: Updated version accepted by Physical Review D

We estimate the efficiency of mitigating the lensing $B$-mode polarization, the so-called delensing, for the $LiteBIRD$ experiment with multiple external data sets of lensing-mass tracers. The current best bound on the tensor-to-scalar ratio, $r$, is limited by lensing rather than Galactic foregrounds. Delensing will be a critical step to improve sensitivity to $r$ as measurements of $r$ become more and more limited by lensing. In this paper, we extend the analysis of the recent $LiteBIRD$ forecast paper to include multiple mass tracers, i.e., the CMB lensing maps from $LiteBIRD$ and CMB-S4-like experiment, cosmic infrared background, and galaxy number density from $Euclid$- and LSST-like survey. We find that multi-tracer delensing will further improve the constraint on $r$ by about $20\%$. In $LiteBIRD$, the residual Galactic foregrounds also significantly contribute to uncertainties of the $B$-modes, and delensing becomes more important if the residual foregrounds are further reduced by an improved component separation method., Comment: 21 pages, 7 figures

We explore the capability of measuring lensing signals in $LiteBIRD$ full-sky polarization maps. With a $30$ arcmin beam width and an impressively low polarization noise of $2.16\,\mu$K-arcmin, $LiteBIRD$ will be able to measure the full-sky polarization of the cosmic microwave background (CMB) very precisely. This unique sensitivity also enables the reconstruction of a nearly full-sky lensing map using only polarization data, even considering its limited capability to capture small-scale CMB anisotropies. In this paper, we investigate the ability to construct a full-sky lensing measurement in the presence of Galactic foregrounds, finding that several possible biases from Galactic foregrounds should be negligible after component separation by harmonic-space internal linear combination. We find that the signal-to-noise ratio of the lensing is approximately $40$ using only polarization data measured over $90\%$ of the sky. This achievement is comparable to $Planck$'s recent lensing measurement with both temperature and polarization and represents a four-fold improvement over $Planck$'s polarization-only lensing measurement. The $LiteBIRD$ lensing map will complement the $Planck$ lensing map and provide several opportunities for cross-correlation science, especially in the northern hemisphere.

We revisit the flat-sky approximation for evaluating the angular power spectra of projected random fields by retaining information about the correlations along the line of sight. With broad, overlapping radial window functions, these line-of-sight correlations are suppressed and are ignored in the Limber approximation. However, retaining the correlations is important for narrow window functions or unequal-time spectra but introduces significant computational difficulties due to the highly oscillatory nature of the integrands involved. We deal with the integral over line-of-sight wave-modes in the flat-sky approximation analytically, using the FFTlog expansion of the 3D power spectrum. This results in an efficient computational method, which is a substantial improvement compared to any full-sky approaches. We apply our results to galaxy clustering (with and without redshift-space distortions), CMB lensing and galaxy lensing observables. For clustering, we find excellent agreement with the full-sky results on large (percent-level agreement) and intermediate or small (subpercent agreement) scales, dramatically out-performing the Limber approximation for both wide and narrow window functions, and in equal- and unequal-time cases. In the case of lensing, we show on the full sky that the angular power spectrum of the convergence can be very well approximated by projecting the 3D Laplacian (rather than the correct angular Laplacian) of the gravitational potential, even on large scales. Combining this approximation with our flat-sky techniques provides an efficient and accurate evaluation of the CMB lensing angular power spectrum on all scales., Comment: 36 pages, 13 figures. Submitted to JCAP

Perturbation theory is a powerful tool for studying large-scale structure formation in the universe and calculating observables such as the power spectrum or bispectrum. However, beyond linear order, typically this is done by assuming a simplification in the time-dependence of gravitational-coupling kernels between the matter and velocity fluctuations. Though the true dependencies are known for Lambda cold dark matter cosmologies, they are ignored due to the computational costs associated with considering them in full and, instead, are replaced by simpler dependencies valid for an Einstein--de-Sitter cosmology. Here we develop, implement and demonstrate the effectiveness of a new numerical method for finding the full dynamical evolution of these kernels to all perturbative orders based upon spectral methods using Chebyshev polynomials. This method is found to be orders of magnitude more efficient than direct numerical solvers while still producing highly accurate and reliable results. A code implementation of the Chebyshev spectral method is then presented and characterised. The code has been made publicly available alongside this paper. We expect our method to be of use for interpretation of upcoming galaxy clustering measurements., Comment: 18 pages, 9 figures, 1 table, submitted to PRD

We present cosmological constraints from a gravitational lensing mass map covering 9400 sq. deg. reconstructed from CMB measurements made by the Atacama Cosmology Telescope (ACT) from 2017 to 2021. In combination with BAO measurements (from SDSS and 6dF), we obtain the amplitude of matter fluctuations $\sigma_8 = 0.819 \pm 0.015$ at 1.8% precision, $S_8\equiv\sigma_8({\Omega_{\rm m}}/0.3)^{0.5}=0.840\pm0.028$ and the Hubble constant $H_0= (68.3 \pm 1.1)\, \text{km}\,\text{s}^{-1}\,\text{Mpc}^{-1}$ at 1.6% precision. A joint constraint with CMB lensing measured by the Planck satellite yields even more precise values: $\sigma_8 = 0.812 \pm 0.013$, $S_8\equiv\sigma_8({\Omega_{\rm m}}/0.3)^{0.5}=0.831\pm0.023$ and $H_0= (68.1 \pm 1.0)\, \text{km}\,\text{s}^{-1}\,\text{Mpc}^{-1}$. These measurements agree well with $\Lambda$CDM-model extrapolations from the CMB anisotropies measured by Planck. To compare these constraints to those from the KiDS, DES, and HSC galaxy surveys, we revisit those data sets with a uniform set of assumptions, and find $S_8$ from all three surveys are lower than that from ACT+Planck lensing by varying levels ranging from 1.7-2.1$\sigma$. These results motivate further measurements and comparison, not just between the CMB anisotropies and galaxy lensing, but also between CMB lensing probing $z\sim 0.5-5$ on mostly-linear scales and galaxy lensing at $z\sim 0.5$ on smaller scales. We combine our CMB lensing measurements with CMB anisotropies to constrain extensions of $\Lambda$CDM, limiting the sum of the neutrino masses to $\sum m_{\nu} < 0.13$ eV (95% c.l.), for example. Our results provide independent confirmation that the universe is spatially flat, conforms with general relativity, and is described remarkably well by the $\Lambda$CDM model, while paving a promising path for neutrino physics with gravitational lensing from upcoming ground-based CMB surveys., Comment: 32 pages, 17 figures, replaced with version accepted in ApJ (Feb 2024). Cosmological likelihood data and mass maps are public here: https://lambda.gsfc.nasa.gov/product/act/actadv_prod_table.html ; likelihood software is here: https://github.com/ACTCollaboration/act_dr6_lenslike . Also see companion papers Qu et al and MacCrann et al

We present new measurements of cosmic microwave background (CMB) lensing over $9400$ sq. deg. of the sky. These lensing measurements are derived from the Atacama Cosmology Telescope (ACT) Data Release 6 (DR6) CMB dataset, 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 ($43\sigma$ significance) using a novel pipeline that minimizes sensitivity to foregrounds and to noise properties. To ensure our results are robust, we analyze an extensive set of null tests, consistency tests, and systematic error estimates and employ a blinded analysis framework. The baseline spectrum is well fit by a lensing amplitude of $A_{\mathrm{lens}}=1.013\pm0.023$ relative to the Planck 2018 CMB power spectra best-fit $\Lambda$CDM model and $A_{\mathrm{lens}}=1.005\pm0.023$ relative to the $\text{ACT DR4} + \text{WMAP}$ best-fit model. From our lensing power spectrum measurement, we derive constraints on the parameter combination $S^{\mathrm{CMBL}}_8 \equiv \sigma_8 \left({\Omega_m}/{0.3}\right)^{0.25}$ of $S^{\mathrm{CMBL}}_8= 0.818\pm0.022$ from ACT DR6 CMB lensing alone and $S^{\mathrm{CMBL}}_8= 0.813\pm0.018$ when combining ACT DR6 and Planck NPIPE CMB lensing power spectra. These results are in excellent agreement with $\Lambda$CDM model constraints from Planck or $\text{ACT DR4} + \text{WMAP}$ CMB power spectrum measurements. Our lensing measurements from redshifts $z\sim0.5$--$5$ are thus fully consistent with $\Lambda$CDM structure growth predictions based on CMB anisotropies probing primarily $z\sim1100$. We find no evidence for a suppression of the amplitude of cosmic structure at low redshifts, Comment: 45+22 pages, 50 figures. v2 matches with published version in ApJ. Cosmological likelihood data and lensing maps are here: https://lambda.gsfc.nasa.gov/product/act/actadv_prod_table.html ; likelihood software is here: https://github.com/ACTCollaboration/act_dr6_lenslike . Also see companion papers Madhavacheril et al and MacCrann et al

Weak gravitational lensing by the intervening large-scale structure (LSS) of the Universe is the leading non-linear effect on the anisotropies of the cosmic microwave background (CMB). The integrated line-of-sight mass that causes the distortion -- known as lensing convergence -- can be reconstructed from the lensed temperature and polarization anisotropies via estimators quadratic in the CMB modes, and its power spectrum has been measured from multiple CMB experiments. Sourced by the non-linear evolution of structure, the bispectrum of the lensing convergence provides additional information on late-time cosmological evolution complementary to the power spectrum. However, when trying to estimate the summary statistics of the reconstructed lensing convergence, a number of noise-biases are introduced, as previous studies have shown for the power spectrum. Here, we explore for the first time the noise-biases in measuring the bispectrum of the reconstructed lensing convergence. We compute the leading noise-biases in the flat-sky limit and compare our analytical results against simulations, finding excellent agreement. Our results are critical for future attempts to reconstruct the lensing convergence bispectrum with real CMB data., Comment: 40 pages (including refs), 19 figures, comments very welcome

Reconstruction of gravitational lensing effects in the CMB from current and upcoming surveys is still dominated by temperature anisotropies. Extragalactic foregrounds in temperature maps can induce significant biases in the lensing power spectrum obtained with the standard quadratic estimators. Techniques such as masking cannot remove these foregrounds fully, and the residuals can still lead to large biases if unaccounted for. In this paper, we study the "shear-only" estimator, an example of a class of geometric methods that suppress extragalactic foreground contamination while making only minimal assumptions about foreground properties. The shear-only estimator has only been formulated in the flat-sky limit and so is not easily applied to wide surveys. Here, we derive the full-sky version of the shear-only estimator and its generalisation to an $m=2$ multipole estimator that has improved performance for lensing reconstruction on smaller scales. The multipole estimator is generally not separable, and so is expensive to compute. We explore separable approximations based on a singular-value decomposition, which allow efficient evaluation of the estimator with real-space methods. Finally, we apply these estimators to simulations that include extragalactic foregrounds and verify their efficacy in suppressing foreground biases., Comment: v2 matches with published version

Our view of the last-scattering surface in the cosmic microwave background (CMB) is obscured by secondary anisotropies, sourced by scattering, extragalactic emission and gravitational processes between recombination and observation. Whilst it is established that non-Gaussianity from the correlation between the integrated-Sachs-Wolfe (ISW) effect and gravitational lensing can significantly bias primordial non-Gaussianity (PNG) searches, recent work by Hill (2018) has suggested that other combinations of secondary anisotropies can also produce significant biases. Building on that work, we use the WebSky and Sehgal et al.(2010) simulations to perform an extensive examination of possible biases to PNG measurements for the local, equilateral and orthogonal shapes. For a Planck-like CMB experiment, without foreground cleaning, we find significant biases from cosmic infrared background (CIB)-lensing and thermal Sunyaev-Zel'dovich (tSZ)-lensing bispectra for the local and orthogonal templates, and from CIB and tSZ bispectra for the equilateral template. For future experiments, such as the Simons Observatory, biases from correlations between the ISW effect and the tSZ and CIB will also become important. Finally we investigate whether foreground-cleaning techniques are able to suppress these biases sufficiently. We find that the majority of these biases are effectively suppressed by the internal-linear-combination method and the total bias to Planck-like and SO-like experiments is less than the $1\,\sigma$ statistical error. However, the small total bias arises from the cancellation of several $1\,\sigma$ biases for Planck-like experiments and $2\,\sigma$ biases for SO-like. As this cancellation is likely sensitive to the precise modelling, to ensure robustness against these biases explicit removal methods should be used, likely at the cost of decreased constraining power.

This is a solicited whitepaper for the Snowmass 2021 community planning exercise. The paper focuses on measurements and science with the Cosmic Microwave Background (CMB). The CMB is foundational to our understanding of modern physics and continues to be a powerful tool driving our understanding of cosmology and particle physics. In this paper, we outline the broad and unique impact of CMB science for the High Energy Cosmic Frontier in the upcoming decade. We also describe the progression of ground-based CMB experiments, which shows that the community is prepared to develop the key capabilities and facilities needed to achieve these transformative CMB measurements., Comment: contribution to Snowmass 2021

This Snowmass 2021 White Paper describes the Cosmic Microwave Background Stage 4 project CMB-S4, which is designed to cross critical thresholds in our understanding of the origin and evolution of the Universe, from the highest energies at the dawn of time through the growth of structure to the present day. We provide an overview of the science case, the technical design, and project plan., Comment: Contribution to Snowmass 2021. arXiv admin note: substantial text overlap with arXiv:1908.01062, arXiv:1907.04473

We introduce and validate a delensing framework for the Simons Observatory (SO), which will be used to improve constraints on inflationary gravitational waves (IGWs) by reducing the lensing noise in measurements of the $B$-modes in CMB polarization. SO will initially observe CMB by using three small aperture telescopes and one large-aperture telescope. While polarization maps from small-aperture telescopes will be used to constrain IGWs, the internal CMB lensing maps used to delens will be reconstructed from data from the large-aperture telescope. Since lensing maps obtained from the SO data will be noise-dominated on sub-degree scales, the SO lensing framework constructs a template for lensing-induced $B$-modes by combining internal CMB lensing maps with maps of the cosmic infrared background from Planck as well as galaxy density maps from the LSST survey. We construct a likelihood for constraining the tensor-to-scalar ratio $r$ that contains auto- and cross-spectra between observed $B$-modes and the lensing $B$-mode template. We test our delensing analysis pipeline on map-based simulations containing survey non-idealities, but that, for this initial exploration, does not include contamination from Galactic and extragalactic foregrounds. We find that the SO survey masking and inhomogeneous and atmospheric noise have very little impact on the delensing performance, and the $r$ constraint becomes $\sigma(r)\approx 0.0015$ which is close to that obtained from the idealized forecasts in the absence of the Galactic foreground and is nearly a factor of two tighter than without delensing. We also find that uncertainties in the external large-scale structure tracers used in our multi-tracer delensing pipeline lead to bias much smaller than the $1\,\sigma$ statistical uncertainties., Comment: 22 pages, 14 figures

The increasing availability of Earth Observation data could transform the use and governance of African rural landscapes, with major implications for the livelihoods and wellbeing of people living in those landscapes. Recent years have seen a rapid increase in the development of EO data applications targeted at stakeholders in African agricultural systems. But there is still relatively little critical scholarship questioning how EO data are accessed, presented, disseminated and used in different socio-political contexts, or of whether this increases or decreases the wellbeing of poorer and marginalized peoples. We highlight three neglected areas in existing EO-for-development research: (i) the imaginaries of 'ideal' future landscapes informing deployments of EO data; (ii) how power relationships in larger EO-for-development networks shape the distribution of costs and benefits; and (iii) how these larger-scale political dynamics interact with local-scale inequalities to influence the resilience of marginalised peoples. We then propose a framework for critical EO-for-development research drawing on recent thinking in critical data studies, ICT4D and political ecology., Comment: In proceedings of the 1st Virtual Conference on Implications of Information and Digital Technologies for Development, 2021

The most promising avenue for detecting primordial gravitational waves from cosmic inflation is through measurements of degree-scale CMB $B$-mode polarisation. This approach must face the challenge posed by gravitational lensing of the CMB, which obscures the signal of interest. Fortunately, the lensing effects can be partially removed by combining high-resolution $E$-mode measurements with an estimate of the projected matter distribution. For near-future experiments, the best estimate of the latter will arise from co-adding internal reconstructions (derived from the CMB itself) with external tracers such as the cosmic infrared background (CIB). In this work, we characterise how foregrounds impact the delensing procedure when CIB intensity, $I$, is used as the matter tracer. We find that higher-point functions of the CIB and Galactic dust such as $\langle BEI \rangle_{c}$ and $\langle EIEI \rangle_{c}$ can, in principle, bias the power spectrum of delensed $B$-modes. To quantify these, we first estimate the dust residuals in currently-available CIB maps and upcoming, foreground-cleaned Simons Observatory CMB data. Then, using non-Gaussian simulations of Galactic dust -- extrapolated to the relevant frequencies, assuming the spectral index of polarised dust emission to be fixed at the value determined by Planck -- we show that the bias to any primordial signal is small compared to statistical errors for ground-based experiments, but might be significant for space-based experiments probing very large angular scales. However, mitigation techniques based on multi-frequency cleaning appear to be very effective. We also show, by means of an analytic model, that the bias arising from the higher-point functions of the CIB itself ought to be negligible., Comment: 21 pages + references & appendices. 12 Figures. Matches version published in MNRAS

LiteBIRD is a JAXA-led Strategic Large-Class mission designed to search for the existence of the primordial gravitational waves produced during the inflationary phase of the Universe, through the measurements of their imprint onto the polarization of the cosmic microwave background (CMB). These measurements, requiring unprecedented sensitivity, will be performed over the full sky, at large angular scales, and over 15 frequency bands from 34GHz to 448GHz. The LiteBIRD instruments consist of three telescopes, namely the Low-, Medium- and High-Frequency Telescope (respectively LFT, MFT and HFT). We present in this paper an overview of the design of the Medium-Frequency Telescope (89-224GHz) and the High-Frequency Telescope (166-448GHz), the so-called MHFT, under European responsibility, which are two cryogenic refractive telescopes cooled down to 5K. They include a continuous rotating half-wave plate as the first optical element, two high-density polyethylene (HDPE) lenses and more than three thousand transition-edge sensor (TES) detectors cooled to 100mK. We provide an overview of the concept design and the remaining specific challenges that we have to face in order to achieve the scientific goals of LiteBIRD., Comment: SPIE Conference

LiteBIRD, the Lite (Light) satellite for the study of B-mode polarization and Inflation from cosmic background Radiation Detection, is a space mission for primordial cosmology and fundamental physics. JAXA selected LiteBIRD in May 2019 as a strategic large-class (L-class) mission, with its expected launch in the late 2020s using JAXA's H3 rocket. LiteBIRD plans to map the cosmic microwave background (CMB) polarization over the full sky with unprecedented precision. Its main scientific objective is to carry out a definitive search for the signal from cosmic inflation, either making a discovery or ruling out well-motivated inflationary models. The measurements of LiteBIRD will also provide us with an insight into the quantum nature of gravity and other new physics beyond the standard models of particle physics and cosmology. To this end, LiteBIRD will perform full-sky surveys for three years at the Sun-Earth Lagrangian point L2 for 15 frequency bands between 34 and 448 GHz with three telescopes, to achieve a total sensitivity of 2.16 micro K-arcmin with a typical angular resolution of 0.5 deg. at 100GHz. We provide an overview of the LiteBIRD project, including scientific objectives, mission requirements, top-level system requirements, operation concept, and expected scientific outcomes., Comment: 20 pages, 9 figures

LiteBIRD has been selected as JAXA's strategic large mission in the 2020s, to observe the cosmic microwave background (CMB) $B$-mode polarization over the full sky at large angular scales. The challenges of LiteBIRD are the wide field-of-view (FoV) and broadband capabilities of millimeter-wave polarization measurements, which are derived from the system requirements. The possible paths of stray light increase with a wider FoV and the far sidelobe knowledge of $-56$ dB is a challenging optical requirement. A crossed-Dragone configuration was chosen for the low frequency telescope (LFT : 34--161 GHz), one of LiteBIRD's onboard telescopes. It has a wide field-of-view ($18^\circ \times 9^\circ$) with an aperture of 400 mm in diameter, corresponding to an angular resolution of about 30 arcminutes around 100 GHz. The focal ratio f/3.0 and the crossing angle of the optical axes of 90$^\circ$ are chosen after an extensive study of the stray light. The primary and secondary reflectors have rectangular shapes with serrations to reduce the diffraction pattern from the edges of the mirrors. The reflectors and structure are made of aluminum to proportionally contract from warm down to the operating temperature at $5\,$K. A 1/4 scaled model of the LFT has been developed to validate the wide field-of-view design and to demonstrate the reduced far sidelobes. A polarization modulation unit (PMU), realized with a half-wave plate (HWP) is placed in front of the aperture stop, the entrance pupil of this system. A large focal plane with approximately 1000 AlMn TES detectors and frequency multiplexing SQUID amplifiers is cooled to 100 mK. The lens and sinuous antennas have broadband capability. Performance specifications of the LFT and an outline of the proposed verification plan are presented., Comment: 21 pages, 14 figures

We present a simple approximation that can speed up the computation of the mode-coupling matrices, which are usually the bottleneck for computing unbiased angular power spectra, as well as their associated covariance matrices, of the cosmic microwave background temperature and polarization anisotropies. The approximation results in the speed up of the MASTER algorithm by more than an order of magnitude with very little loss of precision. We demonstrate the performance on simulations of forthcoming cosmic microwave background surveys such as the Simons Observatory and CMB-S4 for a wide variety of survey window functions., Comment: 10 pages, 7 figures. The code used to produce all results of the paper is publicly available on Github

Efforts to detect a primordial $B$-mode of CMB polarization generated by inflationary gravitational waves ought to mitigate the large variance associated with the $B$-modes produced by gravitational lensing, a process known as delensing. A popular approach to delensing entails building a lensing $B$-mode template by mimicking the lensing operation, either at gradient order or non-perturbatively, using high-resolution $E$-mode observations and some proxy of the lensing potential. By explicitly calculating all contributions to two-loop order in lensing to the power spectrum of $B$-modes delensed with such a template in the noise-free limit, we are able to show that: (i) corrections to the leading-order calculation of the lensing $B$-mode power spectrum only enter at the $O(1)\,\%$ level because of extensive cancellations between large terms at next-to-leading order; (ii) these cancellations would disappear if a gradient-order template were to be built from unlensed or delensed $E$-modes, giving rise to a residual delensing floor of $O(10)\,\%$ of the original power; (iii) new cancellations arise when the lensed $E$-modes are used in the gradient-order template, allowing for the delensing floor to be as low as $O(1)\,\%$ of the original power in practical applications of this method; and (iv) these new cancellations would disappear for a non-perturbative template constructed from the lensed $E$-modes, reintroducing a residual delensing floor of $O(10)\,\%$. We further show that the gradient-order template outperforms the non-perturbative one in realistic scenarios with noisy estimates of the $E$-mode polarization and lensing potential. We therefore recommend that in practical applications of $B$-mode template delensing, where the template is constructed directly from the (filtered) observed $E$-modes, the gradient-order approach should be used rather than a non-perturbative remapping., Comment: 12 pages + references. 5 Figures. Published in PRD as an "Editor's suggestion"

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, from the highest energies at the dawn of time through the growth of structure to the present day. 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 semi-analytic projection tool, targeted explicitly towards 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 semi-analytic 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 $5\sigma$, or, in the absence of a detection, of reaching an upper limit of $r < 0.001$ at $95\%$ CL., Comment: 24 pages, 8 figures, 9 tables, submitted to ApJ. arXiv admin note: text overlap with arXiv:1907.04473