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We implement a simple, main beam correction in the maximum-likelihood, parametric component separation approach, which allows on accounting for different beamwidths of input maps at different frequencies without any preprocessing. We validate the approach on full-sky and cut-sky simulations and discuss the importance and impact of the assumptions and simplifications. We find that, in the cases when the underlying sky model is indeed parametric, the method successfully recovers component spectral parameters and component maps at the pre-defined resolution. The improvement on the precision of the estimated spectral parameters is found to be minor due to the redness of the foreground angular spectra, however the method is potentially more accurate, in particular if the foreground properties display strong, spatial variability, as it does not assume commutation of the beam smoothing and mixing matrix operators. The method permits a reconstruction of the CMB map with a resolution significantly superior to that of the lowest resolution map used in the analysis and with the nearly optimal noise level, facilitating exploitation of the cosmological information contained on angular scales, which would be otherwise inaccessible. The method preserves all the advantages of a pixel-domain implementation of the parametric approach, and, as it deals with the beams in the harmonic domain, it can also straightforwardly account for spatially stationary map-domain noise correlations., Comment: 16 pages, 13 figures

High fidelity separation of astrophysical foreground contributions from the cosmic microwave background (CMB) signal has been recognized as one of the main challenges of modern CMB data analysis, and one which needs to be addressed in a robust way to ensure that the next generation of CMB polarization experiments lives up to its promise. In this work we consider the non-parametric maximum likelihood CMB cleaning approach recently proposed by some of the authors which has been shown to match the performance of standard parametric techniques for simple foreground models, while superseding it in cases where the foregrounds do not exhibit a simple frequency dependence. We present a new implementation of the method in pixel space, extending its functionalities to account for spatial variability of the properties of the foregrounds. We describe the algorithmic details of our approach and its validation against the original code as well as the parametric method for various experimental set-ups and different models of the foreground components. We argue that the method provides a compelling alternative to other state-of-the-art techniques., Comment: 20 pages, 17 figures, matches the published version, link to the package https://github.com/CMBSciPol/MICMAC

Mitigation of the impact of foreground contributions to measurements of Cosmic Microwave Background (CMB) polarization is a crucial step in modern CMB data analysis and is of particular importance for a detection of large-scale CMB $B$ modes. A large variety of techniques, based on different assumptions and aiming at either a full component separation or merely cleaning the foreground signals from the CMB maps, have been described in the literature. In this work, we consider this problem within a unified framework based on the maximum likelihood principle, under the assumption that the signal at each frequency can be represented as a linear mixture of sky templates. We discuss the impact of various additional assumptions on the final outcome of the procedure. We find that the component separation problem can be fully solved in two specific situations: when we either know the frequency scaling of all the components or can correctly model them with a limited number of unknown parameters, as is the case in the parametric component separation techniques; or when we either know the statistical properties of all the components, the foregrounds and CMB, or can correctly model them with a limited number of parameters, as for instance in SMICA-like approaches. However, we also show that much less stringent assumptions are sufficient if we only aim at recovering the cleaned CMB signal. In particular, we discuss a ``minimally informed'' non-parametric method based on maximum likelihood. The method only assumes that the component properties are independent on the sky direction, at least over some region of the sky, and that the CMB covariance is known up to some limited number of parameters. We apply this method to recover the CMB $B$ modes polarization signal in the context of forthcoming CMB experiments and compare its performance with that of the standard parametric... (abridged)

We study a possibility of constraining isotropic cosmic birefringence with help of cosmic microwave background polarisation data in the presence of polarisation angle miscalibration without relying on any assumptions about the Galactic foreground angular power spectra and in particular on their EB correlation. We propose a new analysis framework based on a generalised parametric component separation approach, which accounts simultaneously on the presence of galactic foregrounds, relevant instrumental effects and external priors. We find that upcoming multi-frequency CMB data with appropriate calibration priors will allow producing an instrumental-effect-corrected and foreground-cleaned CMB map, which can be used to estimate the isotropic birefringence angle and the tensor-to-scalar ratio, accounting on statistical and systematic uncertainties incurred during the entire procedure. In particular, in the case of a Simons Observatory-like, three Small Aperture Telescopes, we derive an uncertainty on the birefringence angle of $\sigma(\beta_{b}) = 0.07^\circ$ (0.1$^\circ$), assuming the standard cosmology and calibration priors for all (single) frequency channels with the precision of $\sigma(\alpha_i)= 0.1^\circ$ as aimed at by the near future ground-based experiments. This implies that these experiments could confirm or disprove the recently detected value of $\beta_b=0.35^\circ$ with a significance between $3$ and $5 \sigma$. [abridged version], Comment: 20 pages, 9 figures

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

Forthcoming cosmic microwave background (CMB) polarized anisotropy experiments have the potential to revolutionize our understanding of the Universe and fundamental physics. The sought-after, tale-telling signatures will be however distributed over voluminous data sets which these experiments will collect. These data sets will need to be efficiently processed and unwanted contributions due to astrophysical, environmental, and instrumental effects characterized and efficiently mitigated in order to uncover the signatures. This poses a significant challenge to data analysis methods, techniques, and software tools which will not only have to be able to cope with huge volumes of data but to do so with unprecedented precision driven by the demanding science goals posed for the new experiments. A keystone of efficient CMB data analysis are solvers of very large linear systems of equations. Such systems appear in very diverse contexts throughout CMB data analysis pipelines, however they typically display similar algebraic structures and can therefore be solved using similar numerical techniques. Linear systems arising in the so-called map-making problem are one of the most prominent and common ones. In this work we present a massively parallel, flexible and extensible framework, comprised of a numerical library, MIDAPACK, and a high level code, MAPPRAISER, which provide tools for solving efficiently such systems. The framework implements iterative solvers based on conjugate gradient techniques: enlarged and preconditioned using different preconditioners. We demonstrate the framework on simulated examples reflecting basic characteristics of the forthcoming data sets issued by ground-based and satellite-borne instruments, executing it on as many as 16,384 compute cores. The software is developed as an open source project freely available to the community at: https://github.com/B3Dcmb/midapack ., Comment: 31 pages, 20 figures, Published by Astronomy and Computing

We study different variants of the Gibbs sampler algorithm from the perspective of their applicability to the estimation of power spectra of the cosmic microwave background (CMB) anisotropies. These include approaches studied earlier in the CMB literature as well as new ones which are proposed in this work. We demonstrate all these variants on full and cut sky simulations and compare their performance, assessing both their computational and statistical efficiency. For this we employ a consistent comparison metric, an effective sample size (ESS) per second, commonly used in this context in the statistical literature. We show that one of the proposed approaches, referred to as Centered overrelax, which capitalizes on additional, auxiliary variables to minimize computational time needed per sample, and uses overrelaxation to decorrelate subsequent samples, performs better than the standard Gibbs sampler by a factor between one and two orders of magnitude in the nearly full-sky, satellite-like cases. It therefore potentially provides an interesting alternative to the currently favored approaches.

Reaching the sufficient sensitivity to detect primordial B-modes requires modern CMB polarisation experiments to rely on new technologies, necessary for the deployment of arrays thousands of detectors with a broad frequency coverage and operating them for extended periods of time. This increased complexity of experimental design unavoidably introduces new instrumental and systematic effects, which may impact performance of the new instruments. In this work we extend the standard data analysis pipeline by including a (parametric) model of instrumental effects directly in the data model. We then correct for them in the analysis, accounting for the additional uncertainty in the final results. We embed these techniques within a general, end-to-end formalism for estimating the impact of the instrument and foreground models on constraints on the amplitude of the primordial B-mode signal. We focus on the parametric component separation approach which we generalize to allow for simultaneous estimation of instrumental and foreground parameters. We demonstrate the framework by studying the effects induced by an achromatic half-wave plate (HWP), which lead to a frequency-dependent variation of the instrument polarisation angle, and experimental bandpasses which define observational frequency bands. We assume a typical Stage-3 CMB polarisation experiment, and show that maps recovered from raw data collected at each frequency band will unavoidably be linear mixtures of the Q and U Stokes parameters. We then derive a new generalized data model appropriate for such cases, and extend the component separation approach to account for it. We find that some of the instrumental parameters, in particularly those describing the HWP can be successfully constrained by the data themselves without need for external information, while others, like bandpasses, need to be known with good precision in advance., Comment: 24 pages, 10 figures

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

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 by applying a parametric foreground cleaning approach. We further observe no significant additional bias in the delensed B-mode power spectrum after applying foreground cleaning and are therefore able to obtain an unbiased measurement of the tensor-to-scalar ratio, $r$, after delensing., Comment: 26 pages, 13 figures, comments welcome

We present a measurement of the gravitational lensing deflection power spectrum reconstructed with two seasons cosmic microwave background polarization data from the POLARBEAR experiment. Observations were taken at 150 GHz from 2012 to 2014 which survey three patches of sky totaling 30 square degrees. We test the consistency of the lensing spectrum with a Cold Dark Matter (CDM) cosmology and reject the no-lensing hypothesis at a confidence of 10.9 sigma including statistical and systematic uncertainties. We observe a value of A_L = 1.33 +/- 0.32 (statistical) +/- 0.02 (systematic) +/- 0.07 (foreground) using all polarization lensing estimators, which corresponds to a 24% accurate measurement of the lensing amplitude. Compared to the analysis of the first year data, we have improved the breadth of both the suite of null tests and the error terms included in the estimation of systematic contamination.

We provide an overview of the science case, instrument configuration and project plan for the next-generation ground-based cosmic microwave background experiment CMB-S4, for consideration by the 2020 Decadal Survey., Comment: Project White Paper submitted to the 2020 Decadal Survey, 10 pages plus references. arXiv admin note: substantial text overlap with arXiv:1907.04473

The Simons Observatory (SO) is a ground-based cosmic microwave background (CMB) experiment sited on Cerro Toco in the Atacama Desert in Chile that promises to provide breakthrough discoveries in fundamental physics, cosmology, and astrophysics. Supported by the Simons Foundation, the Heising-Simons Foundation, and with contributions from collaborating institutions, SO will see first light in 2021 and start a five year survey in 2022. SO has 287 collaborators from 12 countries and 53 institutions, including 85 students and 90 postdocs. The SO experiment in its currently funded form ('SO-Nominal') consists of three 0.4 m Small Aperture Telescopes (SATs) and one 6 m Large Aperture Telescope (LAT). Optimized for minimizing systematic errors in polarization measurements at large angular scales, the SATs will perform a deep, degree-scale survey of 10% of the sky to search for the signature of primordial gravitational waves. The LAT will survey 40% of the sky with arc-minute resolution. These observations will measure (or limit) the sum of neutrino masses, search for light relics, measure the early behavior of Dark Energy, and refine our understanding of the intergalactic medium, clusters and the role of feedback in galaxy formation. With up to ten times the sensitivity and five times the angular resolution of the Planck satellite, and roughly an order of magnitude increase in mapping speed over currently operating ("Stage 3") experiments, SO will measure the CMB temperature and polarization fluctuations to exquisite precision in six frequency bands from 27 to 280 GHz. SO will rapidly advance CMB science while informing the design of future observatories such as CMB-S4., Comment: Astro2020 Decadal Project Whitepaper. arXiv admin note: text overlap with arXiv:1808.07445

We present the science case, reference design, and project plan for the Stage-4 ground-based cosmic microwave background experiment CMB-S4., Comment: 287 pages, 82 figures

We present the first measurement of cross-correlation between the lensing potential, reconstructed from cosmic microwave background (CMB) {\it polarization} data, and the cosmic shear field from galaxy shapes. This measurement is made using data from the POLARBEAR CMB experiment and the Subaru Hyper Suprime-Cam (HSC) survey. By analyzing an 11~deg$^2$ overlapping region, we reject the null hypothesis at 3.5$\sigma$\ and constrain the amplitude of the {\bf cross-spectrum} to $\widehat{A}_{\rm lens}=1.70\pm 0.48$, where $\widehat{A}_{\rm lens}$ is the amplitude normalized with respect to the Planck~2018{} prediction, based on the flat $\Lambda$ cold dark matter cosmology. The first measurement of this {\bf cross-spectrum} without relying on CMB temperature measurements is possible due to the deep POLARBEAR map with a noise level of ${\sim}$6\,$\mu$K-arcmin, as well as the deep HSC data with a high galaxy number density of $n_g=23\,{\rm arcmin^{-2}}$. We present a detailed study of the systematics budget to show that residual systematics in our results are negligibly small, which demonstrates the future potential of this cross-correlation technique., Comment: 16 pages, 5 figures, Accepted for publication in ApJ

The hot dense environment of the early universe is known to have produced large numbers of baryons, photons, and neutrinos. These extreme conditions may have also produced other long-lived species, including new light particles (such as axions or sterile neutrinos) or gravitational waves. The gravitational effects of any such light relics can be observed through their unique imprint in the cosmic microwave background (CMB), the large-scale structure, and the primordial light element abundances, and are important in determining the initial conditions of the universe. We argue that future cosmological observations, in particular improved maps of the CMB on small angular scales, can be orders of magnitude more sensitive for probing the thermal history of the early universe than current experiments. These observations offer a unique and broad discovery space for new physics in the dark sector and beyond, even when its effects would not be visible in terrestrial experiments or in astrophysical environments. A detection of an excess light relic abundance would be a clear indication of new physics and would provide the first direct information about the universe between the times of reheating and neutrino decoupling one second later., Comment: 5 pages + references; 1 figure; science white paper submitted to the Astro2020 decadal survey

Our current understanding of the Universe is established through the pristine measurements of structure in the cosmic microwave background (CMB) and the distribution and shapes of galaxies tracing the large scale structure (LSS) of the Universe. One key ingredient that underlies cosmological observables is that the field that sources the observed structure is assumed to be initially Gaussian with high precision. Nevertheless, a minimal deviation from Gaussianityis perhaps the most robust theoretical prediction of models that explain the observed Universe; itis necessarily present even in the simplest scenarios. In addition, most inflationary models produce far higher levels of non-Gaussianity. Since non-Gaussianity directly probes the dynamics in the early Universe, a detection would present a monumental discovery in cosmology, providing clues about physics at energy scales as high as the GUT scale., Comment: 5 pages + references; Submitted to the Astro2020 call for science white papers. This version: fixed author list

We study the performance of a typical near-future full sky CMB space mission, aiming at the characterization of the large scale $B$-modes polarization anisotropies with precision on $r\sim 0.001$, after a map-based parametric cleaning of galactic dust and synchrotron, and in the case of spatially varying astrophysical spectral emission laws. Ignoring the spatial variability of the spectral emission laws may result in a bias on $r$ as high as $\mathcal{O}(0.01)$ for realistic models of the variability. However, we show that the component separation formalism can be extended to suppress this bias efficiently. We demonstrate this within the context of the semianalytic formalism of~\citep{Stompor2016}, which we generalize to such cases and use it to propagate the foreground residuals to a cosmological likelihood on tensor-to-scalar ratio, $r$. In particular, we investigate the effects due to introducing extra, independent sets of scaling parameters for different sky areas and including additional scaling parameters per sky area. We then show that the residuals resulting in such cases can be efficiently described with help of extra terms introduced in a model of the covariance of the component-separated CMB maps and which lead to suppression of the bias on $r$ down to the level lower than the expected statistical uncertainty. We discuss how these additional terms can be constructed self-consistently from the available data., Comment: 17 pages, 10 figures

The Simons Observatory (SO) is a new cosmic microwave background experiment being built on Cerro Toco in Chile, due to begin observations in the early 2020s. We describe the scientific goals of the experiment, motivate the design, and forecast its performance. SO will measure the temperature and polarization anisotropy of the cosmic microwave background in six frequency bands: 27, 39, 93, 145, 225 and 280 GHz. The initial configuration of SO will have three small-aperture 0.5-m telescopes (SATs) and one large-aperture 6-m telescope (LAT), with a total of 60,000 cryogenic bolometers. Our key science goals are to characterize the primordial perturbations, measure the number of relativistic species and the mass of neutrinos, test for deviations from a cosmological constant, improve our understanding of galaxy evolution, and constrain the duration of reionization. The SATs will target the largest angular scales observable from Chile, mapping ~10% of the sky to a white noise level of 2 $\mu$K-arcmin in combined 93 and 145 GHz bands, to measure the primordial tensor-to-scalar ratio, $r$, at a target level of $\sigma(r)=0.003$. The LAT will map ~40% of the sky at arcminute angular resolution to an expected white noise level of 6 $\mu$K-arcmin in combined 93 and 145 GHz bands, overlapping with the majority of the LSST sky region and partially with DESI. With up to an order of magnitude lower polarization noise than maps from the Planck satellite, the high-resolution sky maps will constrain cosmological parameters derived from the damping tail, gravitational lensing of the microwave background, the primordial bispectrum, and the thermal and kinematic Sunyaev-Zel'dovich effects, and will aid in delensing the large-angle polarization signal to measure the tensor-to-scalar ratio. The survey will also provide a legacy catalog of 16,000 galaxy clusters and more than 20,000 extragalactic sources., Comment: This paper presents an overview of the Simons Observatory science goals, details about the instrument will be presented in a companion paper. The author contribution to this paper is available at https://simonsobservatory.org/publications.php (Abstract abridged) -- matching version published in JCAP

An estimation of the sky signal from streams of Time Ordered Data (TOD) acquired by Cosmic Microwave Background (\cmb) experiments is one of the most important steps in the context of \cmb data analysis referred to as the map-making problem. The continuously growing \cmb data sets render the \cmb map-making problem more challenging in terms of computational cost and memory in particular in the context of ground based experiments. In this context, we study a novel class of the Preconditioned Conjugate Gradient (PCG) solvers which invoke two-level preconditioners. We compare them against PCG solvers commonly used in the map-making context considering their precision and time-to-solution. We compare these new methods on realistic, simulated data sets reflecting the characteristics of current and forthcoming \cmb ground-based experiment. We develop an embarrassingly parallel implementation of the approach where each processor performs a sequential map-making for a subset of the TOD. We find that considering the map level residuals the new class of solvers permits achieving tolerance of up to 3 orders of magnitude better than the standard approach, where the residual level often saturates before convergence is reached. This corresponds to an important improvement in the precision of recovered power spectra in particular on the largest angular scales. The new method also typically requires fewer iterations to reach a required precision and thus shorter runtimes for a single map-making solution. However, the construction of an appropriate two-level preconditioner can be as costly as a single standard map-making run. Nevertheless, if the same problem needs to be solved multiple times, e.g., as in Monte Carlo simulations, this cost has to be incurred only once, and the method should be competitive not only as far as its precision but also its performance is concerned., Comment: 15 pages, 10 figures, 2 tables

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 uncertainties include both systematic and statistical effects and are averaged over the instrumental noise and CMB signal realizations. The framework can be further extended to account self-consistently for existing uncertainties in the foreground models. We demonstrate and validate the framework on simple study cases which aim at estimating the tensor-to-scalar ratio, r. The proposed approach is computationally efficient permitting an investigation of hundreds of set-ups and foreground models on a single CPU., Comment: 19 pages, 5 figures

Analysis of cosmic microwave background (CMB) datasets typically requires some filtering of the raw time-ordered data. Filtering is frequently used to minimize the impact of low frequency noise, atmospheric contributions and/or scan synchronous signals on the resulting maps. In this work we explicitly construct a general filtering operator, which can unambiguously remove any set of unwanted modes in the data, and then amend the map-making procedure in order to incorporate and correct for it. We show that such an approach is mathematically equivalent to the solution of a problem in which the sky signal and unwanted modes are estimated simultaneously and the latter are marginalized over. We investigate the conditions under which this amended map-making procedure can render an unbiased estimate of the sky signal in realistic circumstances. We then study the effects of time-domain filtering on the noise correlation structure in the map domain, as well as impact it may have on the performance of the popular pseudo-spectrum estimators. We conclude that although maps produced by the proposed estimators arguably provide the most faithful representation of the sky possible given the data, they may not straightforwardly lead to the best constraints on the power spectra of the underlying sky signal and special care may need to be taken to ensure this is the case. By contrast, simplified map-makers which do not explicitly correct for time-domain filtering, but leave it to subsequent steps in the data analysis, may perform equally well and be easier and faster to implement. We focus on polarization-sensitive measurements targeting the B-mode component of the CMB signal and apply the proposed methods to realistic simulations based on characteristics of an actual CMB polarization experiment, POLARBEAR., Comment: 26 pages

The E and B Experiment (EBEX) is a balloon-borne polarimeter designed to measure the polarization of the cosmic microwave background radiation and to characterize the polarization of galactic dust. EBEX was launched December 29, 2012 and circumnavigated Antarctica observing $\sim$6,000 square degrees of sky during 11 days at three frequency bands centered around 150, 250 and 410 GHz. EBEX was the first experiment to operate a kilo-pixel array of transition-edge sensor bolometers and a continuously rotating achromatic half-wave plate aboard a balloon platform. It also pioneered the use of detector readout based on digital frequency domain multiplexing. We describe the temperature calibration of the experiment. The gain response of the experiment is calibrated using a two-step iterative process. We use signals measured on passes across the Galactic plane to convert from readout-system counts to power. The effective smoothing scale of the EBEX optics and the star camera-to-detector offset angles are determined through \c{hi}2 minimization using the compact HII region RCW 38. This two-step process is initially performed with parameters measured before the EBEX 2013 flight and then repeated until the calibration factor and parameters converge., Comment: 6 pages, 3 figures, Proceedings of the 14th Marcel Grossman Conference

We extend a general maximum likelihood foreground estimation for cosmic microwave background polarization data to include estimation of instrumental systematic effects. We focus on two particular effects: frequency band measurement uncertainty, and instrumentally induced frequency dependent polarization rotation. We assess the bias induced on the estimation of the $B$-mode polarization signal by these two systematic effects in the presence of instrumental noise and uncertainties in the polarization and spectral index of Galactic dust. Degeneracies between uncertainties in the band and polarization angle calibration measurements and in the dust spectral index and polarization increase the uncertainty in the extracted CMB $B$-mode power, and may give rise to a biased estimate. We provide a quantitative assessment of the potential bias and increased uncertainty in an example experimental configuration. For example, we find that with 10\% polarized dust, tensor to scalar ratio of $r=0.05$, and the instrumental configuration of the EBEX balloon payload, the estimated CMB $B$-mode power spectrum is recovered without bias when the frequency band measurement has 5% uncertainty or less, and the polarization angle calibration has an uncertainty of up to 4$^{\circ}$., Comment: Accepted for publication in The Astrophysical Journal

Estimation of the sky signal from sequences of time ordered data is one of the key steps in Cosmic Microwave Background (CMB) data analysis, commonly referred to as the map-making problem. Some of the most popular and general methods proposed for this problem involve solving generalised least squares (GLS) equations with non-diagonal noise weights given by a block-diagonal matrix with Toeplitz blocks. In this work we study new map-making solvers potentially suitable for applications to the largest anticipated data sets. They are based on iterative conjugate gradient (CG) approaches enhanced with novel, parallel, two-level preconditioners. We apply the proposed solvers to examples of simulated non-polarised and polarised CMB observations, and a set of idealised scanning strategies with sky coverage ranging from nearly a full sky down to small sky patches. We discuss in detail their implementation for massively parallel computational platforms and their performance for a broad range of parameters characterising the simulated data sets. We find that our best new solver can outperform carefully-optimised standard solvers used today by a factor of as much as 5 in terms of the convergence rate and a factor of up to $4$ in terms of the time to solution, and to do so without significantly increasing the memory consumption and the volume of inter-processor communication. The performance of the new algorithms is also found to be more stable and robust, and less dependent on specific characteristics of the analysed data set. We therefore conclude that the proposed approaches are well suited to address successfully challenges posed by new and forthcoming CMB data sets., Comment: 19 pages // Final version submitted to A&A

EBEX is a balloon-borne telescope designed to measure the polarization of the cosmic microwave background radiation. During its eleven day science flight in the Austral Summer of 2012, it operated 955 spider-web transition edge sensor (TES) bolometers separated into bands at 150, 250 and 410 GHz. This is the first time that an array of TES bolometers has been used on a balloon platform to conduct science observations. Polarization sensitivity was provided by a wire grid and continuously rotating half-wave plate. The balloon implementation of the bolometer array and readout electronics presented unique development requirements. Here we present an outline of the readout system, the remote tuning of the bolometers and Superconducting QUantum Interference Device (SQUID) amplifiers, and preliminary current noise of the bolometer array and readout system., Comment: 15 pages, 12 figures, SPIE conference proceedings

PRISM (Polarized Radiation Imaging and Spectroscopy Mission) was proposed to ESA in May 2013 as a large-class mission for investigating within the framework of the ESA Cosmic Vision program a set of important scientific questions that require high resolution, high sensitivity, full-sky observations of the sky emission at wavelengths ranging from millimeter-wave to the far-infrared. PRISM's main objective is to explore the distant universe, probing cosmic history from very early times until now as well as the structures, distribution of matter, and velocity flows throughout our Hubble volume. PRISM will survey the full sky in a large number of frequency bands in both intensity and polarization and will measure the absolute spectrum of sky emission more than three orders of magnitude better than COBE FIRAS. The aim of this Extended White Paper is to provide a more detailed overview of the highlights of the new science that will be made possible by PRISM, Comment: Figure 8 replaced by the correct version, affiliations of authors added, and minor changes to match the published JCAP version

PRISM (Polarized Radiation Imaging and Spectroscopy Mission) was proposed to ESA in response to the Call for White Papers for the definition of the L2 and L3 Missions in the ESA Science Programme. PRISM would have two instruments: (1) an imager with a 3.5m mirror (cooled to 4K for high performance in the far-infrared---that is, in the Wien part of the CMB blackbody spectrum), and (2) an Fourier Transform Spectrometer (FTS) somewhat like the COBE FIRAS instrument but over three orders of magnitude more sensitive. Highlights of the new science (beyond the obvious target of B-modes from gravity waves generated during inflation) made possible by these two instruments working in tandem include: (1) the ultimate galaxy cluster survey gathering 10e6 clusters extending to large redshift and measuring their peculiar velocities and temperatures (through the kSZ effect and relativistic corrections to the classic y-distortion spectrum, respectively) (2) a detailed investigation into the nature of the cosmic infrared background (CIB) consisting of at present unresolved dusty high-z galaxies, where most of the star formation in the universe took place, (3) searching for distortions from the perfect CMB blackbody spectrum, which will probe a large number of otherwise inaccessible effects (e.g., energy release through decaying dark matter, the primordial power spectrum on very small scales where measurements today are impossible due to erasure from Silk damping and contamination from non-linear cascading of power from larger length scales). These are but a few of the highlights of the new science that will be made possible with PRISM., Comment: 20 pages Latex

We study accuracy, robustness and self-consistency of pixel-domain simulations of the gravitational lensing effect on the primordial CMB anisotropies due to the large-scale structure of the Universe. In particular, we investigate dependence of the results precision on some crucial parameters of such techniques and propose a semi-analytic framework to determine their values so the required precision is a priori assured and the numerical workload simultaneously optimized. Our focus is on the B-mode signal but we discuss also other CMB observables, such as total intensity, T, and E-mode polarization, emphasizing differences and similarities between all these cases. Our semi-analytic considerations are backed up by extensive numerical results. Those are obtained using a code, nicknamed lenS2HAT -- for Lensing using Scalable Spherical Harmonic Transforms (S2HAT) -- which we have developed in the course of this work. The code implements a version of the pixel-domain approach of Lewis (2005) and permits performing the simulations at very high resolutions and data volumes, thanks to its efficient parallelization provided by the S2HAT library -- a parallel library for a calculation of the spherical harmonic transforms. The code is made publicly available., Comment: 20 pages, 14 figures, submitted to A&A, matches version accepted for publication in A&A

We discuss methods for estimating EB and TB spectra of the Cosmic Microwave Background anisotropy maps covering limited sky area. Such odd-parity correlations are expected to vanish whenever parity is not broken. As this is indeed the case in the standard cosmologies, any evidence to the contrary would have a profound impact on our theories of the early Universe. Such correlations could also become a sensitive diagnostic of some particularly insidious instrumental systematics. In this work we introduce three different unbiased estimators based on the so-called standard and pure pseudo-spectrum techniques and later assess their performance by means of extensive Monte Carlo simulations performed for different experimental configurations. We find that a hybrid approach combining a pure estimate of B-mode multipoles with a standard one for E-mode (or T) multipoles, leads to the smallest error bars for both EB (or TB respectively) spectra as well as for the three other polarization-related angular power spectra i.e. EE, BB and TE$. However, if both E and B multipoles are estimated using the pure technique the loss of precision for the EB spectrum is not larger than ~30%. Moreover, for the experimental configurations considered here, the statistical uncertainties -- due to sampling variance and instrumental noise -- of the pseudo-spectrum estimates is at most a factor ~1.4 for TT, EE and TE spectra and a factor ~2 for BB, TB and EB spectra, higher than the most optimistic Fisher estimate of the variance., Comment: 23 pages, 10 figures, submitted for publication to Physical Review D

We study the effects of astrophysical foregrounds on the ability of CMB B-mode polarization experiments to constrain the primordial tensor-to-scalar ratio, r. To clean the foreground contributions we use parametric, maximum likelihood component separation technique, and consider experimental setups optimized to render a minimal level of the foreground residuals in the recovered CMB map. We consider nearly full-sky observations, include two diffuse foreground components, dust and synchrotron, and study cases with and without calibration errors, spatial variability of the foreground properties, and partial or complete B-mode lensing signal removal. In all these cases we find that in the limit of very low noise level and in the absence of the intrumental or modeling systematic effects, the foreground residuals do not lead to a limit on the lowest detectable value of r. But the need to control the foreground residuals will play a major role in determining the minimal noise levels necessary to permit a robust detection of r < 0.1 and therefore in optimizing and forecasting the performance of the future missions. For current and proposed experiments noise levels, the foreground residuals are found non-negligible and potentially can affect our ability to set constraints on r. We also show how the constraints can be significantly improved on by restricting the post component separation processing to a smaller sky area. This procedure applied to a case of a COrE-like satellite mission is shown to result potentially in over an order of magnitude improvement in the detectable value of r. With sufficient knowledge of the experimental bandpasses as well as foreground component scaling laws, our conclusions are found to be independent on the assumed overall normalization of the foregrounds and only quantitatively depend on specific parametrizations assumed for the foreground components., Comment: 5 pages, 2 figures

We present a formalism for performance forecasting and optimization of future cosmic microwave background (CMB) experiments. We implement it in the context of nearly full sky, multifrequency, B-mode polarization observations, incorporating statistical uncertainties due to the CMB sky statistics, instrumental noise, as well as the presence of the foreground signals. We model the effects of a subtraction of these using a parametric maximum likelihood technique and optimize the instrumental configuration with predefined or arbitrary observational frequency channels, constraining either a total number of detectors or a focal plane area. We showcase the proposed formalism by applying it to two cases of experimental setups based on the CMBpol and COrE mission concepts looked at as dedicated B-mode experiments. We find that, if the models of the foregrounds available at the time of the optimization are sufficiently precise, the procedure can help to either improve the potential scientific outcome of the experiment by a factor of a few, while allowing one to avoid excessive hardware complexity, or simplify the instrument design without compromising its science goals. However, our analysis also shows that even if the available foreground models are not considered to be sufficiently reliable, the proposed procedure can guide a design of more robust experimental setups. While better suited to cope with a plausible, greater complexity of the foregrounds than that foreseen by the models, these setups could ensure science results close to the best achievable, should the models be found to be correct., Comment: (26 pages, 14 figures, has been published in the 15 September 2011 issue of Physical Review D (Vol.84, No.6))

We describe an algorithm for computing an inverse spherical harmonic transform suitable for graphic processing units (GPU). We use CUDA and base our implementation on a Fortran90 routine included in a publicly available parallel package, S2HAT. We focus our attention on the two major sequential steps involved in the transforms computation, retaining the efficient parallel framework of the original code. We detail optimization techniques used to enhance the performance of the CUDA-based code and contrast them with those implemented in the Fortran90 version. We also present performance comparisons of a single CPU plus GPU unit with the S2HAT code running on either a single or 4 processors. In particular we find that use of the latest generation of GPUs, such as NVIDIA GF100 (Fermi), can accelerate the spherical harmonic transforms by as much as 18 times with respect to S2HAT executed on one core, and by as much as 5.5 with respect to S2HAT on 4 cores, with the overall performance being limited by the Fast Fourier transforms. The work presented here has been performed in the context of the Cosmic Microwave Background simulations and analysis. However, we expect that the developed software will be of more general interest and applicability.

EBEX is a NASA-funded balloon-borne experiment designed to measure the polarization of the cosmic microwave background (CMB). Observations will be made using 1432 transition edge sensor (TES) bolometric detectors read out with frequency multiplexed SQuIDs. EBEX will observe in three frequency bands centered at 150, 250, and 410 GHz, with 768, 384, and 280 detectors in each band, respectively. This broad frequency coverage is designed to provide valuable information about polarized foreground signals from dust. The polarized sky signals will be modulated with an achromatic half wave plate (AHWP) rotating on a superconducting magnetic bearing (SMB) and analyzed with a fixed wire grid polarizer. EBEX will observe a patch covering ~1% of the sky with 8' resolution, allowing for observation of the angular power spectrum from \ell = 20 to 1000. This will allow EBEX to search for both the primordial B-mode signal predicted by inflation and the anticipated lensing B-mode signal. Calculations to predict EBEX constraints on r using expected noise levels show that, for a likelihood centered around zero and with negligible foregrounds, 99% of the area falls below r = 0.035. This value increases by a factor of 1.6 after a process of foreground subtraction. This estimate does not include systematic uncertainties. An engineering flight was launched in June, 2009, from Ft. Sumner, NM, and the long duration science flight in Antarctica is planned for 2011. These proceedings describe the EBEX instrument and the North American engineering flight., Comment: 12 pages, 9 figures, Conference proceedings for SPIE Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy V (2010)

How did the universe evolve? The fine angular scale (l>1000) temperature and polarization anisotropies in the CMB are a Rosetta stone for understanding the evolution of the universe. Through detailed measurements one may address everything from the physics of the birth of the universe to the history of star formation and the process by which galaxies formed. One may in addition track the evolution of the dark energy and discover the net neutrino mass. We are at the dawn of a new era in which hundreds of square degrees of sky can be mapped with arcminute resolution and sensitivities measured in microKelvin. Acquiring these data requires the use of special purpose telescopes such as the Atacama Cosmology Telescope (ACT), located in Chile, and the South Pole Telescope (SPT). These new telescopes are outfitted with a new generation of custom mm-wave kilo-pixel arrays. Additional instruments are in the planning stages., Comment: Science White Paper submitted to the US Astro2010 Decadal Survey. Full list of 177 author available at http://cmbpol.uchicago.edu

In this work we study the relevance of the component separation technique based on the Independent Component Analysis (ICA) and investigate its performance in the context of a limited sky coverage observation and from the viewpoint of our ability to differentiate between cosmological models with different primordial B-mode content. We focus on the low Galactic emission sky patch, corresponding to the target of several operating and planned CMB experiments and which, in many respects, adequately represents a typical "clean" high latitude sky. We consider two fiducial observations, one operating at low (40, 90 GHz) and one at high (150, 350 GHz) frequencies and thus dominated by the synchrotron and thermal dust emission, respectively. We use a parallel version of the FASTICA code to explore a substantial parameter space including Gaussian pixel noise level, observed sky area and the amplitude of the foreground emission and employ large Monte Carlo simulations to quantify errors and biases pertinent to the reconstruction for different choices of the parameter values. We identify a large subspace of the parameter space for which the quality of the CMB reconstruction is excellent. For both the cosmological models, with and without the primordial gravitational waves, we find that FASTICA performs extremely well even in the cases when the B mode CMB signal is up to a few times weaker than the foreground contamination and the noise amplitude is comparable with the total CMB polarized emission. In addition we discuss limiting cases of the noise and foreground amplitudes, for which the ICA approach fails., Comment: 19 pages, 12 figures, 5 tables, replaced to match published version

MAXIMA is a balloon-borne platform for measuring the anisotropy of the Cosmic Microwave Background (CMB). It has measured the CMB power spectrum with a ten-arcminute FWHM beam, corresponding to a detection of the power spectrum out to spherical harmonic multipole l~1000. The spectrum is consistent with a flat Universe with a nearly scale-invariant initial spectrum of adiabatic density fluctuations. Moreover, the MAXIMA data are free from any notable non-Gaussian contamination and from foreground dust emission. In the same region, the WMAP experiment observes the same structure as that observed by MAXIMA, as evinced by analysis of both maps and power spectra. The next step in the evolution of the MAXIMA program is MAXIPOL, which will observe the polarization of the CMB with comparable resolution and high sensitivity over a small patch of the sky., Comment: To appear in New Astronomy Reviews, Proceedings of the CMBNET Meeting, 20-21 February, 2003, Oxford, UK

Gravitational interaction of cosmic microwave background (CMB) photons with matter perturbations present along the line-of-sight to the surface of last scattering modifies the shape of the CMB anisotropy power spectrum. Here I focus on (linear) integrated Sachs-Wolfe and (non-linear) gravitational lensing effects and discuss the detectability of the resulting distortions and their possible consequences for the CMB-based estimation of cosmological parameters. Specifically, I discuss if any of those effects may allow us to use CMB experiments to put independent constraints on the curvature of the universe and the cosmological constant, i.e. breaking the so-called geometrical degeneracy in CMB parameter estimation discussed by Bond, Efstathiou and Tegmark (1997) and Zaldarriaga, Spergel and Seljak (1997). I address that issue using the Fisher matrix approach and show that gravitational lensing of the CMB temperature and polarisation patterns might be detectable by the Planck Surveyor satellite, leading to useful independent and precise constraints on the cosmological constant and spatial curvature. The integrated Sachs-Wolfe effect though bound to restrict those parameters only very weakly still may set constraints more stringent than those currently available., Comment: 6 pages, 2 PS figures, submitted to the UIMP98 Santander workshop proceedings, typos corrected, references added

The Simons Observatory (SO) is a ground-based cosmic microwave background (CMB) experiment sited on Cerro Toco in the Atacama Desert in Chile that promises to provide breakthrough discoveries in fundamental physics, cosmology, and astrophysics. Supported by the Simons Foundation, the Heising-Simons Foundation, and with contributions from collaborating institutions, SO will see first light in 2021 and start a five year survey in 2022. SO has 287 collaborators from 12 countries and 53 institutions, including 85 students and 90 postdocs. The SO experiment in its currently funded form (‘SO-Nominal’) consists of three 0.4 m Small Aperture Telescopes (SATs) and one 6 m Large Aperture Telescope (LAT). Optimized for minimizing systematic errors in polarization measurements at large angular scales, the SATs will perform a deep, degree-scale survey of 10% of the sky to search for the signature of primordial gravitational waves. The LAT will survey 40% of the sky with arc-minute resolution. These observations will measure (or limit) the sum of neutrino masses, search for light relics, measure the early behavior of Dark Energy, and refine our understanding of the intergalactic medium, clusters and the role of feedback in galaxy formation. With up to ten times the sensitivity and five times the angular resolution of the Planck satellite, and roughly an order of magnitude increase in mapping speed over currently operating (“Stage 3”) experiments, SO will measure the CMB temperature and polarization fluctuations to exquisite precision in six frequency bands from 27 to 280 GHz. SO will rapidly advance CMB science while informing the design of future observatories such as CMB-S4. Construction of SO-Nominal is fully funded, and operations and data analysis are funded for part of the planned five-year observations. We will seek federal funding to complete the observations and analysis of SO-Nominal, at the $25M level. The SO has a low risk and cost efficient upgrade path – the 6 m LAT can accommodate almost twice the baseline number of detectors and the SATs can be duplicated at low cost. We will seek funding at the $75M level for an expansion of the SO (‘SO-Enhanced’) that fills the remaining focal plane in the LAT, adds three SATs, and extends operations by five years, substantially improving our science return. By this time SO may be operating as part of the larger CMB-S4 project. This white paper summarizes and extends material presented in, which describes the science goals of SO-Nominal, and which describe the instrument design.