We investigate the impact of instrumental systematic errors in interferometric measurements of the cosmic microwave background (CMB) temperature and polarization power spectra. We simulate interferometric CMB observations to generate mock visibilities and estimate power spectra using the statistically optimal maximum likelihood technique. We define a quadratic error measure to determine allowable levels of systematic error that do not induce power spectrum errors beyond a given tolerance. As an example, in this study we focus on differential pointing errors. The effects of other systematics can be simulated by this pipeline in a straightforward manner. We find that, in order to accurately recover the underlying B-modes for r=0.01 at 28<l<384, Gaussian-distributed pointing errors must be controlled to 0.7^\circ rms for an interferometer with an antenna configuration similar to QUBIC, in agreement with analytical estimates. Only the statistical uncertainty for 28<l<88 would be changed at ~10% level. With the same instrumental configuration, we find the pointing errors would slightly bias the 2-σupper limit of the tensor-to-scalar ratio r by ~10%. We also show that the impact of pointing errors on the TB and EB measurements is negligibly small.
We present results from an end-to-end simulation pipeline interferometric observations of cosmic microwave background polarization. We use both maximum-likelihood and Gibbs sampling techniques to estimate the power spectrum. In addition, we use Gibbs sampling for image reconstruction from interferometric visibilities. The results indicate the level to which various systematic errors (e.g., pointing errors, gain errors, beam shape errors, cross- polarization) must be controlled in order to successfully detect and characterize primordial B modes as well as other scientific goals. In addition, we…
We propose an algorithm for the reconstruction of the signal induced by cosmic strings in the cosmic microwave background (CMB), from radio-interferometric data at arcminute resolution. Radio interferometry provides incomplete and noisy Fourier measurements of the string signal, which exhibits sparse or compressible magnitude of the gradient due to the Kaiser-Stebbins (KS) effect. In this context the versatile framework of compressed sensing naturally applies for solving the corresponding inverse problem. Our algorithm notably takes advantage of a model of the prior statistical distribution of…
We use convolutional neural networks (CNNs) and recurrent neural networks (RNNs) to estimate the parameters of strong gravitational lenses from interferometric observations. We explore multiple strategies and find that the best results are obtained when the effects of the dirty beam are first removed from the images with a deconvolution performed with an RNN-based structure before estimating the parameters. For this purpose, we use the recurrent inference machine (RIM) introduced in Putzky & Welling (2017). This provides a fast and automated alternative to the traditional CLEAN algorithm. We o…
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 polariza…
One of the major targets for next-generation cosmic microwave background (CMB) experiments is the detection of the primordial B-mode signal. Planning is under way for Stage-IV experiments that are projected to have instrumental noise small enough to make lensing and foregrounds the dominant source of uncertainty for estimating the tensor-to-scalar ratio $r$ from polarization maps. This makes delensing a crucial part of future CMB polarization science. In this paper we present a likelihood method for estimating the tensor-to-scalar ratio $r$ from CMB polarization observations, which combines th…
We explore the low-l likelihood of the angular spectrum C(l) of masked CMB temperature maps using an adaptive importance sampler. We find that, in spite of a partial sky coverage, the likelihood distribution of each C(l) closely follows an inverse gamma distribution. Our exploration is accurate enough to measure the inverse gamma parameters along with the correlation between multipoles. Those quantities are used to build an approximation of the joint posterior distribution of the low-l likelihood. The accuracy of the proposed approximation is established using both statistical criteria and a m…
The B-mode polarization of the cosmic microwave background (CMB) provides a unique window into tensor perturbations from inflationary gravitational waves. Survey effects complicate the estimation and description of the power spectrum on the largest angular scales. The pixel-space likelihood yields parameter distributions without the power spectrum as an intermediate step, but it does not have the large suite of tests available to power spectral methods. Searches for primordial B-modes must rigorously reject and rule out contamination. Many forms of contamination vary or are uncorrelated across…
Every experiment is affected by systematic effects that hamper the data analysis and have the potential to ultimately degrade its performance. In the case of probes of the cosmic microwave background (CMB) radiation, a minimal set of issues to consider includes asymmetric beam functions, correlated noise, and incomplete sky coverage. Presuming a simplified scanning strategy that allows for an exact analytical treatment of the problem, we study the impact of systematic effects on the likelihood function of the CMB power spectrum. We use the Fisher matrix, a measure of the information content of…
We describe a method for forecasting errors in interferometric measurements of polarization of the cosmic microwave background (CMB) radiation, based on the use of the Fisher matrix calculated from the visibility covariance and relation matrices. In addition to noise and sample variance, the method can account for many kinds of systematic error by calculating an augmented Fisher matrix, including parameters that characterize the instrument along with the cosmological parameters to be estimated. The method is illustrated with examples of gain errors and errors in polarizer orientation. The augm…
Detection of B-mode polarization of the cosmic microwave background (CMB) radiation is one of the frontiers of observational cosmology. Because they are an order of magnitude fainter than E-modes, it is quite a challenge to detect B-modes. Having more manageable systematics, interferometers prove to have a substantial advantage over imagers in detecting such faint signals. Here, we present a method for Bayesian inference of power spectra and signal reconstruction from interferometric data of the CMB polarization signal by using the technique of Gibbs sampling. We demonstrate the validity of th…
Correlation Calibration: A Hybrid Calibration Technique for Radio Interferometric Arrays
McGill University（麦吉尔大学）；Dunlap Institute for Astronomy and Astrophysics, University of Toronto（多伦多大学邓普勒天文学与天体物理研究所）；Perimeter Institute for Theoretical Physics（基础物理研究所）
We present a Bayesian angular power spectrum and signal map inference engine which can be adapted to interferometric observations of anisotropies inthe cosmic microwave background, 21 cm emission line mapping of galactic brightness fluctuations, or 21 cm absorption line mapping of neutral hydrogen in the dark ages. The method uses Gibbs sampling to generate a sampled representation of the angular power spectrum posterior and the posterior of signal maps given a set of measured visibilities in the uv-plane. We use a mock interferometric CMB observation to demonstrate the validity of this method…
MADmap is a software application used to produce maximum-likelihood images of the sky from time-ordered data which include correlated noise, such as those gathered by Cosmic Microwave Background (CMB) experiments. It works efficiently on platforms ranging from small workstations to the most massively parallel supercomputers. Map-making is a critical step in the analysis of all CMB data sets, and the maximum-likelihood approach is the most accurate and widely applicable algorithm; however, it is a computationally challenging task. This challenge will only increase with the next generation of gr…
We present the exact joint likelihood of pseudo-$C_\ell$ power spectrum estimates measured from an arbitrary number of Gaussian cosmological fields. Our method is applicable to both spin-0 fields and spin-2 fields, including a mixture of the two, and is relevant to Cosmic Microwave Background, weak lensing and galaxy clustering analyses. We show that Gaussian cosmological fields are mixed by a mask in such a way that retains their Gaussianity, without making any assumptions about the mask geometry. We then show that each auto- or cross-pseudo-$C_\ell$ estimator can be written as a quadratic fo…
We extend our maximum likelihood method for reconstructing the cluster-mass cross-correlation from cosmic microwave background (CMB) temperature anisotropies and develop new estimators that utilize six different quadratic combinations of CMB temperature and polarization fields. Our maximum likelihood estimators are constructed with delensed CMB temperature and polarization fields by using an assumed model of the convergence field and they can be iteratively applied to a set of clusters, approaching to the optimal condition for the lensing reconstruction as the assumed initial model is refined.…
Precise reconstruction of the cosmic microwave background lensing potential can be achieved with deep polarization surveys by iteratively removing lensing-induced $B$ modes. We introduce a lensing spectrum estimator and its likelihood for such optimal iterative reconstruction. Our modelling share similarities to the state-of-the-art likelihoods for quadratic estimator-based (QE) lensing reconstruction. In particular, we generalize the $N_L^{(0)}$ and $N_L^{(1)}$ lensing biases, and design a realization-dependent spectrum debiaser, making this estimator robust to uncertainties in the data model…
We develop the XFaster Cosmic Microwave Background (CMB) temperature and polarization anisotropy power spectrum and likelihood technique for the Planck CMB satellite mission. We give an overview of this estimator and its current implementation and present the results of applying this algorithm to simulated Planck data. We show that it can accurately extract the power spectrum of Planck data for the high-l multipoles range. We compare the XFaster approximation for the likelihood to other high-l likelihood approximations such as Gaussian and Offset Lognormal and a low-l pixel-based likelihood. W…
Empirical estimates of the band power covariance matrix are commonly used in cosmic microwave background (CMB) power spectrum analyses. While this approach easily captures correlations in the data, noise in the resulting covariance estimate can systematically bias the parameter fitting. Conditioning the estimated covariance matrix, by applying prior information on the shape of the eigenvectors, can reduce these biases and ensure the recovery of robust parameter constraints. In this work, we use simulations to benchmark the performance of four different conditioning schemes, motivated by contem…
The first measurements of the 21 cm brightness temperature power spectrum from the epoch of reionization will very likely be achieved in the near future by radio interferometric array experiments such as the Hydrogen Epoch of Reionization Array (HERA) and the Square Kilometre Array (SKA). Standard MCMC analyses use an explicit likelihood approximation to infer the reionization parameters from the 21 cm power spectrum. In this paper, we present a new Bayesian inference of the reionization parameters where the likelihood is implicitly defined through forward simulations using density estimation …
The standard model of cosmology, ΛCDM, is the simplest model that matches the current observations, but it relies on two hypothetical components, to wit, dark matter and dark energy. Future galaxy surveys and cosmic microwave background (CMB) experiments will independently shed light on these components, but a joint analysis that includes cross-correlations will be necessary to extract as much information as possible from the observations. In this paper, we carry out a multi-probe analysis based on pseudo-spectra and test it on publicly available data sets. We use CMB temperature anisotropies …
The detection of the primordial $B$-mode spectrum of the polarized cosmic microwave background (CMB) signal may provide a probe of inflation. However, observation of such a faint signal requires excellent control of systematic errors. Interferometry proves to be a promising approach for overcoming such a challenge. In this paper we present a complete simulation pipeline of interferometric observations of CMB polarization, including systematic errors. We employ two different methods for obtaining the power spectra from mock data produced by simulated observations: the maximum likelihood method …
The likelihood function is a crucial element of parameter estimation. In analyses of galaxy overdensities and weak lensing shear, one often approximates the likelihood of the power spectrum with a Gaussian distribution. The posterior probability derived from such a likelihood deviates considerably from the exact posterior on the largest scales probed by any survey, where the central limit theorem does not apply. We show that various forms of Gaussian likelihoods can have a significant impact on the estimation of the primordial non-Gaussianity parameter f_NL from the galaxy angular power spectr…
We present the optimal convergence and shear estimators for lensing reconstruction from the cosmic microwave background temperature field. This generalizes the deflection estimator, is sensitive to non-lensing modes, provides internal consistency checks, and is always at least as optimal. Previously, these estimators were only known in the squeezed limit. This paper decomposes convergence and shear fields into cosine and sine waves and the lensed correlation function is then Taylor expanded in the wave amplitudes. Maximizing the likelihood function gives the optimal estimators for the converge…
Component separation is one of the key stages of any modern, cosmic microwave background (CMB) data analysis pipeline. It is an inherently non-linear procedure and typically involves a series of sequential solutions of linear systems with similar, albeit not identical system matrices, derived for different data models of the same data set. Sequences of this kind arise for instance in the maximization of the data likelihood with respect to foreground parameters or sampling of their posterior distribution. However, they are also common in many other contexts. In this work we consider solving the…
Cosmic Microwave Background (CMB) lensing is a powerful probe of the matter distribution in the Universe. The standard quadratic estimator, which is typically used to measure the lensing signal, is known to be suboptimal for low-noise polarization data from next-generation experiments. In this paper we explain why the quadratic estimator will also be suboptimal for measuring lensing on very small scales, even for measurements in temperature where this estimator typically performs well. Though maximum likelihood methods could be implemented to improve performance, we explore a much simpler solu…
We present the XFaster analysis package. XFaster is a fast, iterative angular power spectrum estimator based on a diagonal approximation to the quadratic Fisher matrix estimator. XFaster uses Monte Carlo simulations to compute noise biases and filter transfer functions and is thus a hybrid of both Monte Carlo and quadratic estimator methods. In contrast to conventional pseudo-$C_\ell$ based methods, the algorithm described here requires a minimal number of simulations, and does not require them to be precisely representative of the data to estimate accurate covariance matrices for the bandpowe…
The Atacama Cosmology Telescope has measured the angular power spectra of microwave fluctuations to arcminute scales at frequencies of 148 and 218 GHz, from three seasons of data. At small scales the fluctuations in the primordial Cosmic Microwave Background (CMB) become increasingly obscured by extragalactic foregounds and secondary CMB signals. We present results from a nine-parameter model describing these secondary effects, including the thermal and kinematic Sunyaev-Zel'dovich (tSZ and kSZ) power; the clustered and Poisson-like power from Cosmic Infrared Background (CIB) sources, and thei…
Accurate and efficient likelihood modeling for large-scale CMB data
Università degli Studi di Ferrara（费拉拉大学）；Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara（意大利国家核物理研究所费拉拉分部）；ICSC, Centro Nazionale “High Performance Computing, Big Data and Quantum Computing”（国家高性能计算、大数据和量子计算中心）；Institut d’Astrophysique Spatiale, CNRS, Univ. Paris-Sud, Université Paris-Saclay（法国国家科学研究中心巴黎第十一大学巴黎萨克雷大学空间天体物理学研究所）
We apply the Karhunen-Loéve methods to cosmic microwave background (CMB) data sets, and show that we can recover the input cosmology and obtain the marginalized likelihoods in $Λ$ cold dark matter cosmologies in under a minute, much faster than Markov chain Monte Carlo methods. This is achieved by forming a linear combination of the power spectra at each multipole $l$, and solving a system of simultaneous equations such that the Fisher matrix is locally unchanged. Instead of carrying out a full likelihood evaluation over the whole parameter space, we need evaluate the likelihood only for the p…
The observed angular correlation function of the cosmic microwave background has previously been reported to be anomalous, particularly when measured in regions of the sky uncontaminated by Galactic emission. Recent work by Efstathiou et al. presents a Bayesian comparison of isotropic theories, casting doubt on the significance of the purported anomaly. We extend this analysis to all anisotropic Gaussian theories with vanishing mean (<delta T> = 0), using the much wider class of models to confirm that the anomaly is not likely to point to new physics. On the other hand if there is any new phys…
One of the main goals of modern cosmic microwave background (CMB) missions is to measure the tensor-to-scalar ratio $r$ accurately to constrain inflation models. Due to ignorance about the reionization history $X_{e}(z)$, this analysis is usually done by assuming an instantaneous reionization $X_{e}(z)$ which, however, can bias the best-fit value of $r$. Moreover, due to the strong mixing of B-mode and E-mode polarizations in cut-sky measurements, multiplying the sky coverage fraction $f_{sky}$ by the full-sky likelihood would not give satisfactory results. In this work, we forecast constraint…
We study the possibility that the universe has compact topologies T^3, T^2 x R^1, or S^1 x R^2 using the seven-year WMAP data. The maximum likelihood 95% confidence intervals for the size L of the compact direction are 1.7 < L/L_0 < 2.1, 1.8 < L/L_0 < 2.0, 1.2 < L/L_0 < 2.1 for the three cases, respectively, where L_0=14.4 Gpc is the distance to the last scattering surface. An infinite universe is compatible with the data at 4.3 sigma. We find using a Bayesian analysis that the most probable universe has topology T^2 x R^1, with L/L_0=1.9.
The kinetic Sunyaev Zel'dovich (kSZ) effect, cosmic microwave background (CMB) temperature anisotropies induced by the scattering of CMB photons from free electrons, will be measured by near-term CMB experiments at high significance. By combining CMB temperature anisotropies with a tracer of structure, such as a galaxy redshift survey, previous literature introduced a number of techniques to reconstruct the radial velocity field. This reconstructed radial velocity field encapsulates the majority of the cosmological information contained in the kSZ temperature anisotropies, and can provide powe…
We present constraints on the number of relativistic species from a joint analysis of cosmic microwave background (CMB) fluctuations and light element abundances (helium and deuterium) compared to big bang nucleosynthesis (BBN) predictions. Our BBN calculations include updates of nuclear rates in light of recent experimental and theoretical information, with the most significant change occuring for the d(p,gamma)^3He cross section. We calculate a likelihood function for BBN theory and observations that accounts for both observational errors and nuclear rate uncertainties and can be easily embe…
The relic gravitational waves (gw) are the cleanest probe of the violent times in the very early history of the Universe. They are expected to leave signatures in the observed cosmic microwave background anisotropies. We significantly improved our previous analysis [1] of the 5-year WMAP $TT$ and $TE$ data at lower multipoles $\ell$. This more general analysis returned essentially the same maximum likelihood (ML) result (unfortunately, surrounded by large remaining uncertainties): the relic gw are present and they are responsible for approximately 20% of the temperature quadrupole. We identify…
