With the temperature power spectrum of the cosmic microwave background (CMB) at least four orders of magnitude larger than the B-mode polarisation power spectrum, any instrumental imperfections that couple temperature to polarisation must be carefully controlled and/or removed. Here we present two new map-making algorithms that can create polarisation maps that are clean of temperature-to-polarisation leakage systematics due to differential gain and pointing between a detector pair. Where a half wave plate is used, we show that the spin-2 systematic due to differential ellipticity can also by removed using our algorithms. The algorithms require no prior knowledge of the imperfections or temperature sky to remove the temperature leakage. Instead, they calculate the systematic and polarisation maps in one step directly from the time ordered data (TOD). The first algorithm is designed to work with scan strategies that have a good range of crossing angles for each map pixel and the second for scan strategies that have a limited range of crossing angles. The first algorithm can also be used to identify if systematic errors that have a particular spin are present in a TOD. We demonstrate the use of both algorithms and the ability to identify systematics with simulations of TOD with realistic scan strategies and instrumental noise.
We discuss a new scale-discretised directional wavelet transform to analyse spin signals defined on the sphere, in particular the polarisation of the cosmic microwave background (CMB).
Robust CMB polarisation mapmaking with a rotating half-wave plate
Université Paris Cité, CNRS, Astroparticule et Cosmologie（巴黎西岱大学，法国国家科学研究中心，粒子与宇宙学）；Jodrell Bank Centre for Astrophysics, University of Manchester（曼彻斯特大学，天体物理学乔德雷尔银行中心）
We present Spin-SILC, a new foreground component separation method that accurately extracts the cosmic microwave background (CMB) polarisation $E$ and $B$ modes from raw multifrequency Stokes $Q$ and $U$ measurements of the microwave sky. Spin-SILC is an internal linear combination method that uses spin wavelets to analyse the spin-2 polarisation signal $P = Q + iU$. The wavelets are additionally directional (non-axisymmetric). This allows different morphologies of signals to be separated and therefore the cleaning algorithm is localised using an additional domain of information. The advantage…
We present the design and performance of a 2x2 prototype array of corrugated feed-horns in W-band. The module is fabricated using a so-called "platelet" technique by milling Aluminum plates. This technique is suitable for low-cost and scalable high performance applications. Room temperature Return Loss measurements show a low (<-30 dB) reflection over a 30% bandwidth with a maximum matching of -42 dB at 100 GHz for all four antennas. Beam pattern measurements indicate good repeatability and a low (-25 dB) sidelobe and crosspolarisation levels. This work is particularly relevant for future Cosm…
We estimate Cosmic Microwave Background (CMB) polarisation power spectra, and temperature-polarisation cross-spectra, from the 9-year data of the Wilkinson Microwave Anisotropy Probe (WMAP). Foreground cleaning is implemented using minimum variance linear combinations of the coefficients of needlet decompositions of sky maps for all WMAP channels, to produce maps for CMB temperature anisotropies (T-mode) and polarisation (E-mode and B-mode), for 9 different years of observation. The final power spectra are computed from averages of all possible cross-year power spectra obtained using foregroun…
We show that the cosmic birefringence and miscalibrated polarisation angles can be determined simultaneously by cosmic microwave background (CMB) experiments using the cross-correlation between $E$- and $B$-mode polarisation data. This is possible because polarisation angles of the CMB are rotated by both the cosmic birefringence and miscalibration effects,whereas those of the Galactic foreground emission only by the latter. Our method does not require prior knowledge of the $E$- and $B$-mode power spectra of the foreground emission, but uses only the knowledge of the CMB polarisation spectra.…
A new spin wavelet transform on the sphere is proposed to analyse the polarisation of the cosmic microwave background (CMB), a spin $\pm 2$ signal observed on the celestial sphere. The scalar directional scale-discretised wavelet transform on the sphere is extended to analyse signals of arbitrary spin. The resulting spin scale-discretised wavelet transform probes the directional intensity of spin signals. A procedure is presented using this new spin wavelet transform to recover E- and B-mode signals from partial-sky observations of CMB polarisation.
In this paper we demonstrate an efficient method for including both CMB temperature and polarisation data in optimal non-Gaussian estimators. The method relies on orthogonalising the multipoles of the temperature and polarisation maps and results in a reduction by a factor of over 3 the terms required to calculate the estimator. The method is illustrated with the modal method applied to bispectrum estimation via the CMB with the trispectrum included as an appendix. However, the method is quite general and can be applied to any optimal bispectrum or trispectrum estimator including the KSW, binn…
A tremendous international effort is currently dedicated to observing the so-called primordial B modes of the Cosmic Microwave Background (CMB) polarisation. If measured, this faint signal imprinted by the primordial gravitational wave background, would be an evidence of the inflation epoch and quantify its energy scale, providing a rigorous test of fundamental physics far beyond the reach of accelerators. At the unprecedented sensitivity level that the new generation of CMB experiments aims to reach, every uncontrolled instrumental systematic effect will potentially result in an analysis bias…
Calibration of CMB Polarisation Using Cross-Experiment Correlations
Laboratory for Theoretical Particle Physics and Cosmology, King’s College London（伦敦国王学院理论粒子物理与宇宙学实验室）；Joseph Henry Laboratories of Physics, Princeton University（普林斯顿大学约瑟夫·亨利物理实验室）
The lack of power anomaly is an intriguing feature at the largest angular scales of the CMB anisotropy temperature pattern, whose statistical significance is not strong enough to claim any new physics beyond the standard cosmological model. We revisit the former statement by also considering polarisation data. We propose a new one-dimensional estimator which takes jointly into account the information contained in the TT, TE and EE CMB spectra. By employing this estimator on Planck 2015 low-$\ell$ data, we find that a random $Λ$CDM realisation is statistically accepted at the level of $3.68 \%$…
Measuring the imprint of primordial gravitational waves in the cosmic microwave background (CMB) polarisation field is one of the main goals in modern cosmology. However, the so called $B$-mode polarisation can be generated by different sources besides the primary one predicted by inflationary theories, known as secondary $B$-mode signal. Among them, CMB lensing and astrophysical foregrounds play an important role. Moreover, a partial sky analysis leads to a leakage between $E$-modes and $B$-modes. In this article, we use the well known Minkowski functionals (MF) statistics to study the signif…
Future Cosmic Microwave Background (CMB) satellite missions aim at using the B-mode polarisation signal to measure the tensor-to-scalar ratio $r$ with a sensitivity $σ(r)$ of the order of $\leq 10^{-3}$. Small uncertainties in the characterisation of instrument properties such as the spectral filters can lead to a leakage of the intensity signal to polarisation and can possibly bias any measurement of a primordial signal. In this paper we discuss methods for avoiding and correcting for the intensity to polarisation leakage due to bandpass mismatch among detector sets. We develop a template fit…
A tremendous international effort is currently dedicated to observing the so-called $B$-modes of the Cosmic Microwave Background (CMB) polarisation. At the unprecedented sensitivity level that the new generation of CMB experiments aims to reach, every uncontrolled instrumental systematic effect will potentially result in an analysis bias that is larger than the much sought-after CMB $B$-mode signal. The absolute calibration of the polarisation angle is particularly important in this sense, as any associated error will end up in a leakage from the much larger $E$ modes into $B$ modes. The Crab …
Asymmetric beams can create significant bias in estimates of the power spectra from CMB experiments. With the temperature power spectrum many orders of magnitude stronger than the B-mode power spectrum any systematic error that couples the two must be carefully controlled and/or removed. Here, we derive unbiased estimators for the CMB temperature and polarisation power spectra taking into account general beams and general scan strategies. A simple consequence of asymmetric beams is that, even with an ideal scan strategy where every sky pixel is seen at every orientation, there will be residual…
The B-mode polarisation power spectrum in the Cosmic Microwave Background (CMB) is about four orders of magnitude fainter than the CMB temperature power spectrum. Any instrumental imperfections that couple temperature fluctuations to B-mode polarisation must therefore be carefully controlled and/or removed. We investigate the role that a scan strategy can have in mitigating certain common systematics by averaging systematic errors down with many crossing angles. We present approximate analytic forms for the error on the recovered B-mode power spectrum that would result from differential gain, …
A local void modifies the sky distribution pattern of the cosmic microwave background (CMB) polarisation by gravitational lensing and produces B-modes from E-modes for an off-center observer. In order to see whether this effect can be used to observationally test the validity of the local void model, we calculate this lensing effect by solving the propagation of CMB polarisation along null geodesics close to the central light cone in the general Lemaître-Tolman-Bondi (LTB) model perturbatively. In particular, we give general formulas for the correlations of E and B observed by an off-center ob…
The 21-cm line fluctuations and the cosmic microwave background (CMB) are powerful probes of the epoch of reionisation of the universe. We study the potential of the cross-correlation between 21-cm line fluctuations and CMB anisotropy to obtain further constraints on the reionisation history. We compute analytically the 21-cm cross-correlation with the CMB temperature anisotropy and polarisation, and we calculate the signal-to-noise (SN) ratio for its detection with Planck together with LOFAR, MWA and SKA. We find, on the one hand, that the 21-cm cross-correlation signal with CMB polarisation …
We impose constraints on the topology of the Universe determined from a search for matched circles in the cosmic microwave background (CMB) temperature anisotropy patterns of the 7-year WMAP data. We pay special attention to the sensitivity of the method to residual foreground contamination of the sky maps. A search for pairs of matched back-to-back circles in the higher resolution WMAP W-band map allows tighter constraints to be imposed on topology. Our results rule out universes with topologies that predict pairs of such circles with radii larger than approximately 10 degrees. This places a …
A cross-calibration approach for polarisation-sensitive detectors in CMB experiments: application to LiteBIRD's polarisation angle calibration
University of Milano Bicocca（米兰比可卡大学）；Dipartimento di Fisica, Università La Sapienza（罗马第一大学物理系）；INFN Sezione di Roma（罗马国家核物理研究所）；Université Grenoble Alpes, CNRS, LPSC-IN2P3（格勒诺布尔阿尔卑斯大学）；Laboratoire de Physique de l’École Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris（巴黎高等师范学院物理实验室）；Dipartimento di Fisica, Università di Roma Tor Vergata（罗马第二大学物理系）；IRAP, Université de Toulouse, CNRS, CNES, UPS（图卢兹大学天体物理与粒子物理研究所）；Instituto de Fisica de Cantabria (IFCA, CSIC-UC)（坎塔布里亚物理研究所）；Dipartimento di Fisica e Astronomia “G. Galilei”, Università degli Studi di Padova（帕多瓦大学伽利略物理与天文系）；INFN Sezione di Padova（帕多瓦国家核物理研究所）
We present new methods for mapping the curl-free (E-mode) and divergence-free (B-mode) components of spin 2 signals using spin directional wavelets. Our methods are equally applicable to measurements of the polarisation of the cosmic microwave background (CMB) and the shear of galaxy shapes due to weak gravitational lensing. We derive pseudo and pure wavelet estimators, where E-B mixing arising due to incomplete sky coverage is suppressed in wavelet space using scale- and orientation-dependent masking and weighting schemes. In the case of the pure estimator, ambiguous modes (which have vanishi…
We present an assessment of the CMB large scale anomalies in polarisation using the two-point correlation function as a test case. We employ the state of the art of large scale polarisation datasets: the first based on a Planck 2018 HFI 100 and 143 GHz cross-spectrum analysis, based on SRoll2 processing, and the second from a map-based approach derived through a joint treatment of Planck 2018 LFI and WMAP-9yr. We consider the well-known $S_{1/2}$ estimator, which measures the distance of the two-point correlation function from zero at angular scales larger than $60^{\circ}$, and rely on realis…
We compute the bispectrum induced in the cosmic microwave background (CMB) temperature and polarisation by the evolution of the primordial density perturbations using the second-order Boltzmann code SONG. We show that adding polarisation increases the signal-to-noise ratio by a factor four with respect to temperature alone and we estimate the observability of this intrinsic bispectrum and the bias it induces on measurements of primordial non-Gaussianity. When including all physical effects except the late-time non-linear evolution, we find for the intrinsic bispectrum a signal-to-noise of $S/N…
The CMB $B$-mode polarisation signal -- both the primordial gravitational wave signature and the signal sourced by lensing -- is subject to many contaminants from systematic effects. Of particular concern are systematics that result in mixing of signals of different ``spin'', particularly leakage from the much larger spin-0 intensity signal to the spin-2 polarisation signal. We present a general formalism, which can be applied to arbitrary focal plane setups, that characterises signals in terms of their spin. We provide general expressions to describe how spin-coupled signals observed by the d…
We study the possibility for constraining the topology of the Universe by means of the matched circles statistic applied to polarised cosmic microwave background (CMB) anisotropy maps. The advantages of using the CMB polarisation maps in studies of the topology over simply analysing the temperature data as has been done to-date are clearly demonstrated. We test our algorithm to search for pairs of matched circles on simulated CMB maps for a universe with the topology of 3-torus. It is found that the noise levels of both Planck and next generation CMB experiments data are no longer prohibitive …
Templates for polarised emission from Galactic foregrounds at frequencies relevant to Cosmic Microwave Background (CMB) polarisation experiments are obtained by modelling the Galactic Magnetic Field (GMF) on large scales. This work extends the results of O'Dea et al. by including polarised synchrotron radiation as a source of foreground emission. The polarisation direction and fraction in this calculation are based solely on the underlying choice of GMF model and therefore provide an independent prediction for the polarisation signal on large scales. Templates of polarised foregrounds may be o…
We develop a method to reconstruct the primordial power spectrum, P(k), using both temperature and polarisation data from the joint analysis of a number of Cosmic Microwave Background (CMB) observations. The method is an extension of the Richardson-Lucy algorithm, first applied in this context by Shafieloo & Souradeep. We show how the inclusion of polarisation measurements can decrease the uncertainty in the reconstructed power spectrum. In particular, the polarisation data can constrain oscillations in the spectrum more effectively than total intensity only measurements. We apply the estimato…
Searches for the imprint of primordial gravitational waves in degree-scale CMB $B$-mode polarisation data must account for significant contamination from gravitational lensing. Fortunately, the lensing effects can be partially removed by combining high-resolution $E$-mode measurements with an estimate of the projected matter distribution. In the near future, experimental characteristics will be such that the latter can be reconstructed internally with high fidelity from the observed CMB, with the $EB$ quadratic estimator providing a large fraction of the signal-to-noise. It is a well-known phe…
Future cosmic microwave background (CMB) polarisation experiments aim to measure an unprecedentedly small signal - the primordial gravity wave component of the polarisation field B-mode. To achieve this, they will analyse huge datasets, involving years worth of time-ordered data (TOD) from massively multi-detector focal planes. This creates the need for fast and precise methods to complement the M-L approach in analysis pipelines. In this paper, we investigate fast map-making methods as applied to long duration, massively multi-detector, ground-based experiments, in the context of the search f…
Cosmic strings generate vector and tensor modes in the B-channel of polarization, as well as the usual temperature power spectrum and E-mode polarization spectrum. We use the power spectrum obtained from high-resolution Nambu-Goto cosmic string simulations together with the Planck and BICEP2 likelihoods to explore the degeneracies appearing between cosmic strings and other cosmological parameters in different inflationary scenarios, as well as the constraints that can be imposed on cosmic strings in each of these situations. In standard $Λ$CDM, the Planck likelihood yields an upper limit $Gμ<1…
Precise polarisation measurements of the cosmic microwave background (CMB) require accurate knowledge of the instrument orientation relative to the sky frame used to define the cosmological Stokes parameters. Suitable celestial calibration sources that could be used to measure the polarimeter orientation angle are limited, so current experiments commonly `self-calibrate.' The self-calibration method exploits the theoretical fact that the $EB$ and $TB$ cross-spectra of the CMB vanish in the standard cosmological model, so any detected $EB$ and $TB$ signals must be due to systematic errors. Howe…
We present a new method for calculating CMB anisotropies in a non-flat Friedmann universe, relying on a very stable algorithm for the calculation of hyperspherical Bessel functions, that can be pushed to arbitrary precision levels. We also introduce a new approximation scheme which gradually takes over in the flat space limit, and significant speeds-up calculations. Our method is implemented in the Boltzmann code CLASS. It can be used to benchmark the accuracy of the CAMB code in curved space, which is found to match expectations. For default precision settings, corresponding to 0.1% for scala…
Many weak lensing calculations make use of the Born approximation where the light ray is approximated by a straight path. We examine the effect of Born-corrections for lensing of the cosmic microwave background in an analytical approach by taking perturbative corrections to the geodesic into account. The resulting extra power in the lensing potential spectrum is comparable to the power generated by nonlinear structure formation and affects especially the polarisation spectra, leading to relative changes of the order of one per cent for the $E$-mode spectrum and up to 10 per cent on all scales …
In this note, we study cosmic microwave background (CMB) constraints on primordial non-Gaussianity in DBI galileon models in which an induced gravity term is added to the Dirac-Born-Infeld (DBI) action. In this model, the non-Gaussianity of orthogonal shape can be generated. We provide a relation between theoretical parameters and orthogonal/equilateral non-linear parameters using the Fisher matrix approach for the CMB bispectrum. In doing so, we include the effect of the CMB transfer functions and experimental noise properties by employing the recently developed \textsf{SONG} code. The relati…
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）
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…
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…
QUBIC (Q \& U Bolometric Interferometer for Cosmology) is an international ground-based experiment dedicated in the measurement of the polarized fluctuations of the Cosmic Microwave Background (CMB). It is based on bolometric interferometry, an original detection technique which combine the immunity to systematic effects of an interferometer with the sensitivity of low temperature incoherent detectors. QUBIC will be deployed in Argentina, at the Alto Chorrillos mountain site near San Antonio de los Cobres, in the Salta province. The QUBIC detection chain consists in 2048 NbSi Transition Edge S…
The observation of the polarised emission from the Cosmic Microwave Background (CMB) from future ground-based and satellite-borne experiments holds the promise of indirectly detecting the elusive signal from primordial tensor fluctuations in the form of large-scale $B$-mode polarisation. Doing so, however, requires an accurate and robust separation of the signal from polarised Galactic foregrounds. We present a component separation method for multi-frequency CMB observations that combines some of the advantages of map-based and power-spectrum-based techniques, and which is direcly applicable t…
Cross-spectra likelihood for robust $τ$ constraints from all satellite polarisation 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）；Institut d’Astrophysique Spatiale, CNRS, Univ. Paris-Sud, Université Paris-Saclay（法国国家科学研究中心天体物理学研究所，巴黎南大学，巴黎萨克雷大学）
One of the main goals of Cosmology is to search for the imprint of primordial gravitational waves in the CMB polarisation field, to probe inflationary theories. One of the obstacles toward the detection of the primordial signal is to extract the B-mode polarisation from astrophysical contaminations. We present a complete analysis of extragalactic foreground contamination due to polarised emission of radio and dusty star-forming galaxies. We update or use up-to-date models that are validated using the most recent measurements. We predict the flux limit (confusion noise) for the future CMB space…
We develop an efficient method based on the linear regression algorithm to probe the cosmological CPT violation using the CMB polarisation data. We validate this method using simulated CMB data and apply it to recent CMB observations. We find that a combined data sample of BICEP1 and BOOMERanG 2003 favours a nonzero isotropic rotation angle at $2.3σ$ confidence level, ie, $Δα=-3.3 \pm1.4$ deg (68% CL) with systematics included.
Future observations of cosmic microwave background (CMB) polarisation have the potential to answer some of the most fundamental questions of modern physics and cosmology. In this paper, we list the requirements for a future CMB polarisation survey addressing these scientific objectives, and discuss the design drivers of the CORE space mission proposed to ESA in answer to the "M5" call for a medium-sized mission. The rationale and options, and the methodologies used to assess the mission's performance, are of interest to other future CMB mission design studies. CORE is designed as a near-ultima…
The properties of the cosmic microwave background (CMB) temperature and polarisation anisotropies measured by a static, off-centered observer located in a local spherically symmetric void, are described. In particular in this paper we compute, together with the standard 2- point angular correlation functions, the off-diagonal correlators, which are no more vanishing by symmetry. While the energy shift induced by the off-centered position of the observer can be suppressed by a proper choice of the observer velocity, a lensing-like effect on the CMB emission point remains. This latter effect is …
Combining a recent derivation of the CMB evolution equations for homogeneous but anisotropic (Bianchi) cosmologies with an account of the full linearized dynamical freedoms available in such models, I calculate and discuss the various temperature and polarisation anisotropy patterns which may be formed. Certain anisotropies can be hidden in superhorizon modes at early times, thus avoiding any constraints from nucleosynthesis while nevertheless producing non-trivial redshift-zero temperature patterns in flat and open universes. The results are likely to be more of pedagogical than observational…
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 sol…
We present new clean maps of the CMB temperature anisotropies (as measured by Planck) constructed with a novel internal linear combination (ILC) algorithm using directional, scale-discretised wavelets --- Scale-discretised, directional wavelet ILC or SILC. Directional wavelets, when convolved with signals on the sphere, can separate the anisotropic filamentary structures which are characteristic of both the CMB and foregrounds. Extending previous component separation methods, which use the frequency, spatial and harmonic signatures of foregrounds to separate them from the cosmological backgrou…
Cosmology has made enormous progress through studies of the cosmic microwave background, however the subtle signals being now sought such as B-mode polarisation due to primordial gravitational waves are increasingly hard to disentangle from residual Galactic foregrounds in the derived CMB maps. We revisit our finding that on large angular scales there are traces of the nearby old supernova remnant Loop I in the WMAP 9-year map of the CMB and confirm this with the new SMICA map from the Planck satellite.
Madam is a CMB map-making code, designed to make temperature and polarization maps of time-ordered data of total power experiments like Planck. The algorithm is based on the destriping technique, but it also makes use of known noise properties in the form of a noise prior. The method in its early form was presented in an earlier work by Keihanen et al. (2005). In this paper we present an update of the method, extended to non-averaged data, and include polarization. In this method the baseline length is a freely adjustable parameter, and destriping can be performed at a different map resolution…
