Extragalactic foregrounds are known to constitute a limiting systematic in temperature-based CMB lensing with AdvACT, SPT-3G, Simons Observatory and CMB S4. Furthermore, since these foregrounds are emitted at cosmological distances, they are also themselves lensed. The correlation between this foreground lensing and CMB lensing causes an additional bias in CMB lensing estimators. In this paper, we quantify for the first time this "lensed foreground bias" for the standard CMB lensing quadratic estimator, the CMB shear and the CMB magnification estimators, in the case of Simons Observatory and in the absence of multi-frequency component separation. This percent-level bias is highly significant in cross-correlation of CMB lensing with LSST galaxies, and comparable to the statistical uncertainty in CMB lensing auto-spectrum. We discuss various mitigation strategies, and show that "lensed foreground bias-hardening" methods can reduce this bias at some cost in signal-to-noise. The code used to generate our theory curves is publicly available at https://github.com/EmmanuelSchaan/LensedForegroundBias .
The CMB polarization promises to unveil the dawn of time measuring the gravitational wave background emitted by the Inflation. The CMB signal is faint, however, and easily contaminated by the Galactic foreground emission, accurate measurements of which are thus crucial to make CMB observations successful. We review the CMB polarization properties and the current knowledge on the Galactic synchrotron emission, which dominates the foregrounds budget at low frequency. We then focus on the S-Band Polarization All Sky Survey (S-PASS), a recently completed survey of the entire southern sky designed …
Polarized Galactic foregrounds are one of the primary sources of systematic error in measurements of the B-mode polarization of the Cosmic Microwave Background (CMB). Experiments are becoming increasingly sensitive to complexities in the foreground frequency spectra that are not captured by standard parametric models, potentially affecting our ability to efficiently separate out these components. Employing a suite of dust models encompassing a variety of physical effects, we simulate observations of a future seven-band CMB experiment to assess the impact of these complexities on parametric com…
We present a new method which leverages conditional Generative Adversarial Networks (cGAN) to reconstruct galaxy cluster convergence from lensed CMB temperature maps. Our model is constructed to emphasize structure and high-frequency correctness relative to the Residual U-Net approach presented by Caldeira, et. al. (2019). Ultimately, we demonstrate that while both models perform similarly in the no-noise regime (as well as after random off-centering of the cluster center), cGAN outperforms ResUNet when processing CMB maps noised with 5uK/arcmin white noise or astrophysical foregrounds (tSZ an…
We demonstrate how to obtain optimal constraints on a primordial gravitational wave component in lensed Cosmic Microwave Background (CMB) data under ideal conditions. We first derive an estimator of the tensor-to-scalar ratio, $r$, by using an error-controlled close approximation to the exact posterior, under the assumption of Gaussian primordial CMB and lensing deflection potential. This combines fast internal iterative lensing reconstruction with optimal recovery of the unlensed CMB. We evaluate its performance on simulated low-noise polarization data targeted at the recombination peak. We c…
Precise measurement of the foreground synchrotron emission, which contaminates the faint polarized cosmic microwave background radiation (CMB), is a major challenge for the next-generation of CMB experiments. To address this, dedicated foreground measurement experiments are being undertaken at radio frequencies between 2 and 40 GHz. Foreground polarized synchrotron emission measurements are particularly challenging, primarily due to the complicated frequency dependence in the presence of Faraday rotation, and are best recovered through broad fractional-bandwidth polarization measurements at fr…
CMB foregrounds consist of all radiation between the surface of last scattering and the detectors, which can interfere with the cosmological interpretation of CMB data. Fortunately, in temperature (intensity), even though the foregrounds are complex they can relatively easily be mitigated. However, in polarization, diffuse Galactic radiation (synchrotron and thermal dust) can be polarized at a level of >10 % making it more of a challenge. In particular, CMB B-modes, which are a smoking-gun signature of inflation, will be dominated by foregrounds. Component separation will therefore be critical…
We propose a method to extract the unlensed, intrinsic CMB temperature and polarization power spectra from the observed (i.e., lensed) spectra. Using a matrix inversion technique, we demonstrate how one can reconstruct the intrinsic CMB power spectra directly from lensed data for both flat sky and full sky analyses. The delensed spectra obtained by the technique are calibrated against the Code for Anisotropies in the Microwave Background (CAMB) using WMAP 7-year best-fit data and applied to WMAP 9-year unbinned data as well. In principle, our methodology may help in subtracting out the E-mode …
$Ab$ $initio$ modeling of Galactic dust polarized CMB foreground
Nanjing University（南京大学）；University of California, San Diego（加州大学圣迭戈分校）；Kavli Institute for Theoretical Physics, University of California, Santa Barbara（加州大学圣巴巴拉分校卡弗里理论物理研究所）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
Gravitational lensing of the Cosmic Microwave Background (CMB) encodes cosmological information in the observed anisotropies of temperature and polarization. Accurate extraction of this additional information requires precise modeling of the covariance matrix of the power spectra of observed CMB fields. We introduce a new analytical model to describe the non-Gaussian structure of this covariance matrix and display the importance of second-order terms that were previously neglected. When compared with direct numerical simulations our model captures parameter errors to better than a few percent …
The cosmic microwave background (CMB) is gravitationally lensed by large-scale structure, which distorts observations of the primordial anisotropies in any given direction. Averaged over the sky, this important effect is routinely modelled with the lensed CMB power spectra. This accounts for the variance of this distortion, where the leading variance effect is quadratic in the lensing deflections. However, we show that if bright extragalactic sources correlated with the large-scale structure are masked in a CMB map, the power spectrum measured over the unmasked area using a standard pseudo-$C_…
Next generation CMB experiments such as CMB-S4 aim at measuring the CMB lensing potential at sub-percent precision where most of the constraining power will come from CMB polarization. We investigate the prospects of achieving this goal in the presence of large-scale, diffuse galactic foreground emission by using non-Gaussian sky simulations and exploit multi-frequency information to clean those. We show that, while prior to foreground cleaning, cosmological parameter estimates from the contaminated lensing potential estimation can be significantly biased, these can be successfully mitigated b…
A promising way to measure the distribution of matter on small scales (k ~ 10 hMpc^-1) is to use gravitational lensing of the Cosmic Microwave Background (CMB). CMB-HD, a proposed high-resolution, low-noise millimeter survey over half the sky, can measure the CMB lensing auto spectrum on such small scales enabling measurements that can distinguish between a cold dark matter (CDM) model and alternative models designed to solve problems with CDM on small scales. However, extragalactic foregrounds can bias the CMB lensing auto spectrum if left untreated. We present a foreground mitigation strateg…
Extracting CMB B-mode polarization from complicated foregrounds is a challenging task in searching for inflationary gravitational waves. We propose the ABS method as a blind and analytical solution to this problem. It applies to the measured cross bandpower between different frequency bands and obtains the CMB B-mode bandpower analytically. It does not rely on assumptions of foregrounds and does not require multiple parameter fitting. Testing against a variety of foregrounds, survey frequency configurations and instrument noise, we verify its applicability and numerical stability. The ABS meth…
This paper provides full sky maps of foreground emission in all WMAP channels, with very low residual contamination from the Cosmic Microwave Background (CMB) anisotropies and controlled level of instrumental noise. Foreground maps are obtained by subtraction of a properly filtered CMB map, obtained from linear combinations of needlet-based representations of all WMAP observations and of a 100-micron map. The error in the reconstructed foreground maps on large scales is significantly lower than the original error due to CMB contamination, while remaining of the order of the original WMAP noise…
In this paper, we try to probe whether a clean CMB map obtained from the raw satellite data using a cleaning procedure is sufficiently clean. Specifically we study if there are any foreground residuals still present in the cleaned data using a cross-correlation statistic. Residual contamination is expected to be present, primarily, in the galactic plane due to the high emission from our own galaxy. A foreground mask is applied conventionally to avoid biases in the estimated quantities of interest due to foreground leakage. Here, we map foreground residuals, if present, in the unmasked region i…
Contribution to the 2026 Cosmology session of the 60th Rencontres de Moriond: Galactic moments: Understanding polarized foregrounds complexity in the quest for CMB primordial $B$ modes with LiteBIRD
Univ Toulouse, CNES, CNRS, IRAP（图卢兹大学，法国国家空间研究中心，法国国家科学研究中心，天体物理研究所）；Université Paris-Saclay, CNRS/IN2P3, IJCLab（巴黎-萨克雷大学，法国国家科学研究中心/法国国家粒子物理研究所，IJCLab）；Instituto de Astrofísica de Canarias（加那利群岛天体物理研究所）；Departamento de Astrofísica, Universidad de La Laguna (ULL)（拉帕拉塔大学天体物理学系）；Department of Physics, University of Oxford（牛津大学物理系）
Polarized foregrounds are going to be a serious challenge for detecting CMB cosmological B-modes. Both diffuse Galactic emission and extragalactic sources contribute significantly to the power spectrum on large angular scales. At low frequencies, Galactic synchrotron emission will dominate with fractional polarization $\sim 20-40%$ at high latitudes while radio sources can contribute significantly even on large ($\sim 1^{\circ}$) angular scales. Nevertheless, simulations suggest that a detection at the level of $r=0.001$ might be achievable if the foregrounds are not too complex.
We present a new approach to component separation in multifrequency CMB experiments by formulating the problem as that of partitioning the sky into pixel clusters such that within each pixel cluster the foregrounds have similar spectrum, using only the information available in the data. Only spectral information is used for partitioning, allowing spatially far away pixels to belong to the same cluster if their foreground properties are close. We then apply a modified internal linear combination method to each pixel cluster. Since the foregrounds have similar spectrum within each cluster, the n…
Recent Planck observations have revealed some of the important statistical properties of synchrotron and dust polarisation, namely, the $B$ to $E$ mode power and temperature-$E$ (TE) mode cross-correlation. In this paper, we extend our analysis in Kandel et al. (2017) that studied $B$ to $E$ mode power ratio for polarised dust emission to include TE cross-correlation and develop an analogous formalism for synchrotron signal, all using a realistic model of magnetohydrodynamical (MHD) turbulence. Our results suggest that the Planck results for both synchrotron and dust polarisation can be unders…
The cosmic microwave background (CMB) is one of the finest probes of cosmology. Its all-sky temperature and linear polarization (LP) fluctuations have been measured precisely at a level of deltaT/TCMB ~10^{-6}. In comparison, circular polarization (CP) of the CMB, however, has not been precisely explored. Current upper limit on the CP of the CMB is at a level of deltaV/TCMB ~10^{-4} and is limited on large scales. Some of the cosmologically important sources which can induce a CP in the CMB include early universe symmetry breaking, primordial magnetic field, galaxy clusters and Pop III stars (…
In this paper we present a new method to estimate a foreground cleaned Cosmic Microwave Background (CMB) map at a resolution of $1^\circ$ by minimizing the non-Gaussian properties of the cleaned map which arise dominantly due to diffuse foreground emission components from the Milky Way. We employ simple kurtosis statistic as the measure of non-Gaussian properties and perform a linear combination of 5 frequency maps provided by Wilkinson Microwave Anisotropy Probe (WMAP) in its 7 year data release in such a way that the cleaned map has a minimum kurtosis which leads to a non-Gaussianity minimiz…
Foreground removal techniques for CMB analyses make specific assumptions about the properties of foregrounds in temperature and in polarization. By investigating the statistics of foreground components more understanding about the degree to which these assumptions are valid can be obtained. In this work we investigate $E$- and $B$-mode maps of the two strongest polarized foregrounds, synchrotron and thermal dust emission, with regards to their similarity with Gaussian processes, their spectral variations and cross-correlations. We perform tests in patches of $\sim3.7^\circ$ size collectively c…
Extragalactic foregrounds are known to generate significant biases in temperature-based CMB lensing reconstruction. Several techniques, which include ``source hardening'' and ``shear-only estimators'' have been proposed to mitigate contamination and have been shown to be very effective at reducing foreground-induced biases. Here we extend both techniques to polarization, which will be an essential component of CMB lensing reconstruction for future experiments, and investigate the ``large-lens'' limit analytically to gain insight on the origin and scaling of foreground biases, as well as the se…
Internal Linear Combination (ILC) methods are some of the most widely used multi-frequency cleaning techniques employed in CMB data analysis. These methods reduce foregrounds by minimizing the total variance in the coadded map (subject to a signal-preservation constraint), although often significant foreground residuals or biases remain. A modification to the ILC method is the constrained ILC (cILC), which explicitly nulls certain foreground components; however, this foreground nulling often comes at a high price for ground-based CMB datasets, with the map noise increasing significantly on sma…
The contribution from the residuals of the foreground can have a significant impact on the temperature maps of the Cosmic Microwave Background (CMB). Mostly, the focus has been on the galactic plane, when foreground cleaning has taken place. However, in this paper, we will investigate the possible foreground contamination, from sources outside the galactic plane in the CMB maps. We will analyze the correlation between the Faraday rotation map and the CMB temperature map. The Faraday rotation map is dependent on the galactic magnetic field, as well as the thermal electron density, and both may …
The measurement of the large-scale B-mode polarization in the cosmic microwave background (CMB) is a fundamental goal of future CMB experiments. However, because of unprecedented sensitivity, future CMB experiments will be much more sensitive to any imperfect modelling of the Galactic foreground polarization in the reconstruction of the primordial B-mode signal. We compare the sensitivity to B-modes of different concepts of CMB satellite missions (LiteBIRD, COrE, COrE+, PRISM, EPIC, PIXIE) in the presence of Galactic foregrounds. In particular, we quantify the impact on the tensor-to-scalar pa…
In order to extract information about inflationary gravitational waves using $B$-mode patterns of cosmic microwave polarization anisotropy, we need to remove the foreground radiation from the Milky Way. In our previous delta-map method for foreground removal, the number of observation bands was limited to the number of parameters of the assumed foreground model, and therefore it was difficult to improve the sensitivity by increasing the number of observation bands. Here, we extend the previous method so that it can be adapted to an arbitrary number of observation bands. Using parametric likeli…
We address a current caveat in the deconvolution of the Primordial Power Spectrum (PPS), from observed Cosmic Microwave Background (CMB) temperature anisotropy, in the presence of weak lensing of the CMB by the large scale structure (LSS) in the Universe. Richardson-Lucy (RL) deconvolution algorithm has been used in the context of reconstructing a free-form PPS, $P_R(k)$ from the observed lensed CMB temperature anisotropy power spectrum $\widetilde{C}_{\ell}^{TT}$. We propose and demonstrate that the RL algorithm works in the context of a non-linear convolution where the non-linear contributio…
CMB lensing from current and upcoming wide-field CMB experiments such as AdvACT, SPT-3G and Simons Observatory relies heavily on temperature (vs. polarization). In this regime, foreground contamination to the temperature map produces significant lensing biases, which cannot be fully controlled by multi-frequency component separation, masking or bias hardening. In this letter, we split the standard CMB lensing quadratic estimator into a new set of optimal "multipole" estimators. On large scales, these multipole estimators reduce to the known magnification and shear estimators, and a new shear B…
We present a new, semi-analytic framework for estimating the level of residuals present in CMB maps derived from multi-frequency Cosmic Microwave Background (CMB) data and forecasting their impact on cosmological parameters. The data are assumed to contain non-negligible signals of astrophysical and/or Galactic origin, which we clean using parametric component separation technique. We account for discrepancies between the foreground model assumed during the separation procedure and the true one, allowing for differences in scaling laws and/or their spatial variations. Our estimates and their u…
The extraction of foreground and CMB maps from multi-frequency observations relies mostly on the different frequency behavior of the different components. Existing Bayesian methods additionally make use of a Gaussian prior for the CMB whose correlation structure is described by an unknown angular power spectrum. We argue for the natural extension of this by using non-trivial priors also for the foreground components. Focusing on diffuse Galactic foregrounds, we propose a log-normal model including unknown spatial correlations within each component and cross-correlations between the different f…
Understanding large-angular-scale galactic foregrounds is crucial for future CMB experiments aiming to detect $B$-mode polarization from primordial gravitational waves. Traditionally, the dust component has been separated using its different frequency dependence. However, using non-CMB observations has potential to increase fidelity and decrease the reconstruction noise. In this exploratory paper we investigate the capability of galactic 21 cm observations to predict the dust foreground in intensity. We train a neural network to predict the dust foreground as measured by the Planck Satellite f…
Blind mitigation of foreground-induced biases on primordial $B$ modes for ground-based CMB experiments
International School for Advanced Studies (SISSA)（国际高等研究院）；Università di Trento（特伦托大学）；INFN Sezione di Trieste（的里雅斯特INFN分部）；IFPU（前沿物理研究所）；Dipartimento di Fisica, Università di Roma “Tor Vergata”（罗马“托维加塔”大学物理系）；INFN Sezione di Roma2（罗马第二INFN分部）
In this paper we estimate diffuse foreground minimized Cosmic Microwave Background (CMB) Stokes Q and U polarization maps based upon the fundamental concept of Gaussian nature of CMB and strong non-Gaussian nature of astrophysical polarized foregrounds using WMAP nine year published polarization maps. We excise regions of the sky that define position of the known point sources, regions that are strongly contaminated by either the detector noise or by the diffuse foregrounds or both, and then perform foreground minimizations over the surviving sky regions that constitute approximately $50\%$ of…
Galactic foregrounds are the main obstacle to observations of the cosmic microwave background (CMB) $B$-mode polarization. In addition to obscuring the inflationary $B$-mode signal by several orders of magnitude, Galactic foregrounds have non-trivial spectral signatures that are partially unknown and distorted by averaging effects along the line-of-sight, within the pixel/beam window, and by various analysis choices (e.g., spherical harmonic transforms and filters). Statistical moment expansion methods provide a powerful tool for modeling the effective Galactic foreground emission resulting fr…
One of the primary challenges facing upcoming CMB polarization experiments aiming to measure the inflationary B-mode signal is the removal of polarized foregrounds. The thermal dust foreground is often modeled as a single modified blackbody, however overly simplistic foreground models can bias measurements of the tensor-to-scalar ratio r. As CMB polarization experiments become increasingly sensitive, thermal dust emission models must account for greater complexity in the dust foreground while making minimal assumptions about the underlying distribution of dust properties within a beam. We use …
Future high-sensitivity measurements of the cosmic microwave background (CMB) anisotropies and energy spectrum will be limited by our understanding and modeling of foregrounds. Not only does more information need to be gathered and combined, but also novel approaches for the modeling of foregrounds, commensurate with the vast improvements in sensitivity, have to be explored. Here, we study the inevitable effects of spatial averaging on the spectral shapes of typical foreground components, introducing a moment approach, which naturally extends the list of foreground parameters that have to be d…
We study a strategy to determine miscalibrated polarization angles of cosmic microwave background (CMB) experiments using the observed $EB$ polarization power spectra of CMB and Galactic foreground emission. We apply the methodology of Minami et al.(2019) developed for full-sky observations to ground-based experiments such as Simons Observatory. We take into account the $E$-to-$B$ leakage and $\ell$-to-$\ell$ covariance due to partial sky coverage using the public code NaMaster. We show that our method yields an unbiased estimate of miscalibrated angles. Our method also enables simultaneous de…
We extend the ILC method in harmonic space to include the error in its CMB estimate. This allows parameter estimation routines to take into account the effect of the foregrounds as well as the errors in their subtraction in conjunction with the ILC method. Our method requires the use of a model of the foregrounds which we do not develop here. The reduction of the foreground level makes this method less sensitive to unaccounted for errors in the foreground model. Simulations are used to validate the calculations and approximations used in generating this likelihood function.
Reconstructed maps of the lensing convergence of the cosmic microwave background (CMB) will play a major role in precision cosmology in coming years. CMB lensing maps will enable calibration of the masses of high-redshift galaxy clusters and will yield precise measurements of the growth of cosmic structure through cross-correlations with galaxy surveys. During the next decade, CMB lensing reconstruction will rely heavily on temperature data, rather than polarization, thus necessitating a detailed understanding of biases due to extragalactic foregrounds. In the near term, the most significant b…
We extend the internal template foreground removal method by accounting for spatially varying spectral parameters such as the spectral indices of synchrotron and dust emission and the dust temperature. As the previous algorithm had to assume that the spectral parameters are uniform over the full sky (or some significant fraction of the sky), it resulted in a bias in the tensor-to-scalar ratio parameter $r$ estimated from foreground-cleaned polarization maps of the cosmic microwave background (CMB). The new algorithm, "Delta-map method", accounts for spatially varying spectra to first order in …
[Abridged] Recent results from the BICEP, Keck Array and Planck Collaborations demonstrate that Galactic foregrounds are an unavoidable obstacle in the search for evidence of inflationary gravitational waves in the cosmic microwave background (CMB) polarization. Beyond the foregrounds, the effect of lensing by intervening large-scale structure further obscures all but the strongest inflationary signals permitted by current data. With a plethora of ongoing and upcoming experiments aiming to measure these signatures, careful and self-consistent consideration of experiments' foreground- and lensi…
We reconstruct shear maps and angular power spectra from simulated weakly lensed total intensity (TT) and polarised (EB) maps of the Cosmic Microwave Background (CMB) anisotropies, obtained using Born approximated ray-tracing through the N-body simulated Cold Dark Matter (CDM) structures in the Millennium Simulations (MS). We compare the recovered signal with the $Λ$CDM prediction, on the whole interval of angular scales which is allowed by the finite box size, extending from the degree scale to the arcminute, by applying a quadratic estimator in the flat sky limit; we consider PRISM-like inst…
Cosmic baryon evolution during the Cosmic Dawn and Reionization results in redshifted 21-cm spectral distortions in the cosmic microwave background (CMB). These encode information about the nature and timing of first sources over redshifts 30-6 and appear at meter wavelengths as a tiny CMB distortion along with the Galactic and extragalactic radio sky, which is orders of magnitude brighter. Therefore, detection requires precise methods to model foregrounds. We present a method of foreground fitting using maximally smooth (MS) functions. We demonstrate the usefulness of MS functions over tradit…
Upcoming measurements of the small-scale primary cosmic microwave background (CMB) temperature and polarization power spectra ($TT$/$TE$/$EE$) are anticipated to yield transformative constraints on new physics, including the effective number of relativistic species in the early universe ($N_{\rm eff}$). However, at multipoles $\ell \gtrsim 3000$, the primary CMB power spectra receive significant contributions from gravitational lensing. While these modes still carry primordial information, their theoretical modeling requires knowledge of the CMB lensing convergence power spectrum, $C_L^{κκ}$, …
Recent CMB observations have resulted in very precise observational data. A robust and reliable CMB reconstruction technique can lead to efficient estimation of the cosmological parameters. We demonstrate the performance of our methodology using simulated temperature and polarization observations using cosmic variance limited future generation PRISM satellite mission. We generate samples from the joint distribution by implementing the CMB inverse covariance weighted internal-linear-combination (ILC) with the Gibbs sampling technique. We use the Python Sky Model (PySM), d4f1s1 to generate the r…
Science opportunities and recommendations concerning optical/infrared polarimetry for the upcoming decade in the field of cosmology. Community-based White Paper to Astro2010 in response to the call for such papers.
The constraints on departures from general relativity (GR) at cosmological length scales due to cosmic microwave background (CMB) data are discussed. The departure from GR is measured by the ratio, parameterized as $1 +\varpi_0 (1 + z)^{-S}$, between the gravitational potentials conventionally appearing in the geodesic equation and the Poisson equation. Current CMB data indicate $\varpi_0=1.67^{+3.07}_{-1.87}$ at the 2$σ$ confidence level, while $S$ remains unconstrained. The departure from GR affects the lensing conversion of E-mode into B-mode polarization. Hence, the lensing measurements fr…
