Excess B‐modes extracted from the Planck polarization maps

One of the main obstacles for extracting the Cosmic Microwave Background (CMB) from mm/submm observations is the pollution from the main Galactic components: synchrotron, free‐free and thermal dust emission. The feasibility of using simple neural networks to extract CMB has been demonstrated on both temperature and polarization data obtained by the WMAP satellite. The main goal of this paper is to demonstrate the feasibility of neural networks for extracting the CMB signal from the Planck polarization data with high precision. Both auto‐correlation and cross‐correlation power spectra within a mask covering about 63 % of the sky have been used together with a “high pass filter” in order to minimize the influence of the remaining systematic errors in the Planck Q and U maps. Using the Planck 2015 released polarization maps, a BB power spectrum have been extracted by Multilayer Perceptron neural networks. This spectrum contains a bright feature with signal to noise ratios 4.5 within 200 ≪ l ≪ 250. The spectrum is significantly brighter than the BICEP2 2015 spectrum, with a spectral behaviour quite different from the “canonical” models (weak lensing plus B‐modes spectra with different tensor to scalar ratios). The feasibility of the neural network to remove the residual systematics from the available Planck polarization data to a high level has been demonstrated. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Foreground removal from Planck Sky Model temperature maps using a MLP neural network

Unfortunately, the Cosmic Microwave Background (CMB) radiation is contaminated by emission originating in the Milky Way (synchrotron, free‐free and dust emission). Since the cosmological information is statistically in nature, it is essential to remove this foreground emission and leave the CMB with no systematic errors. To demonstrate the feasibility of a simple multilayer perceptron (MLP) neural network for extracting the CMB temperature signal, we have analyzed a specific data set, namely the Planck Sky Model maps, developed for evaluation of different component separation methods before including them in the Planck data analysis pipeline. It is found that a MLP neural network can provide a CMB map of about 80 % of the sky to a very high degree uncorrelated with the foreground components. Also the derived power spectrum shows little evidence for systematic errors (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Foreground removal from CMB temperature maps using an MLP neural network

One of the main obstacles for extracting the Cosmic Microwave Background (CMB) signal from observations in the mm-submm range is the foreground contamination by emission from Galactic components: mainly synchrotron, free-free and thermal dust emission. Due to the statistical nature of the intrinsic CMB signal it is essential to minimize the systematic errors in the CMB temperature determinations. Following the available knowledge of the spectral behavior of the Galactic foregrounds simple power law-like spectra have been assumed. The feasibility of using a simple neural network for extracting the CMB temperature signal from the combined signal CMB and the foregrounds has been investigated. As a specific example, we have analysed simulated data, as expected from the ESA Planck CMB mission. A simple multilayer perceptron neural network with 2 hidden layers can provide temperature estimates over more than 80 per cent of the sky that are to a high degree uncorrelated with the foreground signals. A single network will be able to cover the dynamic range of the Planck noise level over the entire sky.     

Separation of foreground and background signals in single frequency measurements of the CMB polarization

The polarization of the Cosmic Microwave Background (CMB) is a powerful observational tool at hand for modern cosmology. It allows to break the degeneracy of fundamental cosmological parameters one cannot obtain using only anisotropy data and provides new insight into conditions existing in the very early Universe. Many experiments are now in progress whose aim is detecting anisotropy and polarization of the CMB. Measurements of the CMB polarization are however hampered by the presence of polarized foregrounds, above all the synchrotron emission of our Galaxy, whose importance increases as frequency decreases and dominates the polarized diffuse radiation at frequencies below ≃50 GHz. In the past the separation of CMB and synchrotron was made combining observations of the same area of sky at different frequencies. In this paper, we show that the statistical properties of the polarized components of the synchrotron and dust foregrounds are different from the statistical properties of the polarized component of the CMB, therefore one can build a statistical estimator which allows to extract the polarized component of the CMB from single frequency data also when the polarized CMB signal is just a fraction of the total polarized signal. Our estimator improves the signal/noise ratio for the polarized component of the CMB and reduces from ≃50 to ≃20 GHz, the frequency above which the polarized component of the CMB can be extracted from single frequency maps of the diffuse radiation.     

Measuring statistical isotropy of CMB anisotropy

The statistical expectation values of the temperature fluctuations and polarization of cosmic microwave background (CMB) are assumed to be preserved under rotations of the sky. We investigate the statistical isotropy (SI) of the CMB maps recently measured by the Wilkinson microwave anisotropy probe (WMAP) using the bipolar spherical harmonic formalism proposed in Hajian and Souradeep [Hajian, A., Souradeep, T. (2003) Astrophys. J. Lett. 597, L5] for CMB temperature anisotropy and extended to CMB polarization in Basak, Hajian and Souradeep [Basak, S., Hajian, A., Souradeep, T. (2006) Phys. Rev. D74, 02130(R)]. The Bipolar Power Spectrum (BiPS) had been measured for the full sky CMB anisotropy maps of the first year WMAP data and now for the recently released three years of WMAP data. We also introduce and measure directional sensitive reduced Bipolar coefficients on the three year WMAP ILC map. Consistent with our published results from first year WMAP data we have no evidence for violation of statistical isotropy on large angular scales. Preliminary analysis of the recently released first WMAP polarization maps, however, indicate significant violation of SI even when the foreground contaminated regions are masked out. Further work is required to confirm a possible cosmic origin and rule out the (more likely) origin in observational artifact such as foreground residuals at high galactic latitude.     

Angular power spectrum of CMB anisotropy from WMAP

The remarkable improvement in the estimates of different cosmological parameters in recent years has been largely spearheaded by accurate measurements of the angular power spectrum of cosmic microwave background (CMB) radiation. This has required removal of foreground contamination as well as detector noise bias with reliability and precision. Recently, a novel model-independent method for the estimation of CMB angular power spectrum from multi-frequency observations has been proposed and implemented on the first year WMAP (WMAP-1) data by Saha et al. [Saha, R., Jain, P., Souradeep, T., 2006. ApJL, 645, L89]. We review the results from WMAP-1 and also present the new angular power spectrum based on three years of the WMAP data (WMAP-3). Previous estimates have depended on foreground templates built using extraneous observational input to remove foreground contamination. This is the first demonstration that the CMB angular spectrum can be reliably estimated with precision from a self contained analysis of the WMAP data. The primary product of WMAP are the observations of CMB in 10 independent difference assemblies (DA) distributed over five frequency bands that have uncorrelated noise. Our method utilizes maximum information available within WMAP data by linearly combining DA maps from different frequencies to remove foregrounds and estimating the power spectrum from the 24 cross-power spectra of clean maps that have independent noise. An important merit of the method is that the expected residual power from unresolved point sources is significantly tempered to a constant offset at large multipoles (in contrast to the l² contribution expected from a Poisson distribution) leading to a small correction at large multipoles. Hence, the power spectrum estimates are less susceptible to uncertainties in the model of point sources.     

Intracluster medium through three years of WMAP

Wilkinson microwave anisotropy probe (WMAP) has provided us with the highest resolution all-sky maps of the cosmic microwave background (CMB). As a result of thermal Sunyaev–Zel’dovich effect, clusters of galaxies are imprinted as tiny, poorly resolved dips on top of primary CMB anisotropies in these maps. Here, I describe different efforts to extract the physics of intracluster medium (ICM) from the sea of primary CMB, through combining WMAP with low-redshift galaxy or X-ray cluster surveys. This finally culminates at a mean (universal) ICM pressure profile, which is for the first time directly constrained from WMAP 3 year maps, and leads to interesting constraints on the ICM baryonic budget.     

Understanding the WMAP Results: Low-Order Multipoles and Dust in the Vicinity of the Solar System

Analyses of the cosmic microwave background (CMB) radiation maps produced by the Wilkinson Microwave Anisotropy Probe (WMAP) have revealed anomalies not predicted by the standard cosmological theory. It has been suggested that a dust cloud in the vicinity of the Solar system may be the cause for these anomalies. In this paper, the thermal emission by particles from two known interplanetary meteoroid complexes is tested against the CMB maps. Conclusions are drawn based on the geometry of cloud projections onto the WMAP sky whether these clouds are likely to explain the observed anomaly. The smooth background Zodiacal cloud and one of the Taurid meteor complex branches do not explain the WMAP anomaly.     

The WMAP data and results

The Wilkinson Microwave Anisotropy Probe (WMAP) science team has released results from the first year of operation at the Earth–Sun L₂ Lagrange point. The maps are consistent with previous observations but have much better sensitivity and angular resolution than the COBE DMR maps, and much better calibration accuracy and sky coverage than ground-based and balloon-borne experiments. The angular power spectra from these ground-based and balloon-borne experiments are consistent within their systematic and statistical uncertainties with the WMAP results. WMAP detected the large angular-scale correlation between the temperature and polarization anisotropies of the CMB caused by electron scattering since the Universe became reionized after the “Dark Ages”, giving a value for the electron scattering optical depth of 0.17 ± 0.04. The simplest ΛCDM model with n=1 and Ω_tot=1 fixed provides an adequate fit to the WMAP data and gives parameters which are consistent with determinations of the Hubble constant and observations of the accelerating Universe using supernovae. The time-ordered data, maps, and power spectra from WMAP can be found at http://lambda.gsfc.nasa.gov along with 13 papers by the WMAP science team describing the results in detail.     

Cross-correlation between WMAP and 2MASS: non-Gaussianity induced by the SZ effect

We study the non-Gaussianity induced by the Sunyaev–Zel'dovich (SZ) effect in cosmic microwave background (CMB) fluctuation maps. If a CMB map is contaminated by the SZ effect of galaxies or galaxy clusters, the CMB maps should have similar non-Gaussian features to the galaxy and cluster fields. Using the WMAP data and 2MASS galaxy catalogue, we show that the non-Gaussianity of the 2MASS galaxies is imprinted on WMAP maps. The signature of non-Gaussianity can be seen with the fourth-order cross-correlation between the wavelet variables of the WMAP maps and 2MASS clusters. The intensity of the fourth-order non-Gaussian features is found to be consistent with the contamination of the SZ effect of 2MASS galaxies. We also show that this non-Gaussianity can not be seen by the high-order autocorrelation of the WMAP . This is because the SZ signals in the autocorrelations of the WMAP data generally are weaker than the WMAP –2MASS cross-correlations by a factor f ², which is the ratio between the powers of the SZ-effect map and the CMB fluctuations on the scale considered. Therefore, the ratio of high-order autocorrelations of CMB maps to cross-correlations of the CMB maps and galaxy field would be effective to constrain the powers of the SZ effect on various scales.     

Bianchi model CMB polarization and its implications for CMB anomalies

We derive the cosmic microwave background (CMB) radiative transfer equation in the form of a multipole hierarchy in the nearly Friedmann–Robertson–Walker limit of homogeneous, but anisotropic, universes classified via their Bianchi type. Compared with previous calculations, this allows a more sophisticated treatment of recombination, produces predictions for the polarization of the radiation and allows for reionization. Our derivation is independent of any assumptions about the dynamical behaviour of the field equations, except that it requires anisotropies to be small back to recombination; this is already demanded by observations.
We calculate the polarization signal in the Bianchi VII _h case, with the parameters recently advocated to mimic the several large-angle anomalous features observed in the CMB. We find that the peak polarization signal is  ∼1.2 μK  for the best-fitting model to the temperature anisotropies, and is mostly confined to multipoles   l < 10  . Remarkably, the predicted large-angle EE and TE power spectra in the Bianchi model are consistent with Wilkinson Microwave Anisotropy Probe ( WMAP ) observations that are usually interpreted as evidence of early reionization. However, the power in B-mode polarization is predicted to be similar to the E-mode power and parity-violating correlations are also predicted by the model; the WMAP non-detection of either of these signals casts further strong doubts on the veracity of attempts to explain the large-angle anomalies with global anisotropy. On the other hand, given that there exist further dynamical degrees of freedom in the VII _h universes that are yet to be compared with CMB observations, we cannot at this time definitively reject the anisotropy explanation.     

Predicting the polarization of the microwave background from the WMAP temperature maps

In this paper, we study how to predict the polarization of the Cosmic Microwave Background (CMB) using knowledge of only the temperature (intensity) and the cross-correlation between temperature and polarization. We derive a “Wiener prediction” method and apply it to the Wilkinson Microwave Anisotropy Probe (WMAP) all-sky CMB temperature maps and to the MAXIMA field.     

Non-Gaussian foreground residuals of the WMAP first-year maps

We investigate the effect of foreground residuals in the WMAP ( Wilkinson Microwave Anisotropy Probe ) data by adding foreground contamination to Gaussian ensembles of cosmic microwave background (CMB) signal and noise maps. We evaluate a set of non-Gaussian estimators on the contaminated ensembles to determine with what accuracy any residual in the data can be constrained using higher-order statistics. We apply the estimators to the raw and cleaned Q -, V - and W -band first-year maps. The foreground subtraction method applied to clean the data in Bennett et al. appears to have induced a correlation between the power spectra and normalized bispectra of the maps which is absent in Gaussian simulations. It also appears to increase the correlation between the  Δℓ= 1  inter-ℓ bispectrum of the cleaned maps and the foreground templates. In a number of cases the significance of the effect is above the 98 per cent confidence level.     

Maximum likelihood algorithm for parametric component separation in cosmic microwave background experiments

We discuss an approach to the component separation of microwave, multifrequency sky maps as those typically produced from cosmic microwave background (CMB) anisotropy data sets. The algorithm is based on the two-step, parametric, likelihood-based technique recently elaborated on by Eriksen et al., where the foreground spectral parameters are estimated prior to the actual separation of the components. In contrast with the previous approaches, we accomplish the former task with help of an analytically derived likelihood function for the spectral parameters, which, we show, yields estimates equal to the maximum likelihood values of the full multidimensional data problem. We then use these estimates to perform the second step via the standard, generalized-least-squares-like procedure. We demonstrate that the proposed approach is equivalent to a direct maximization of the full data likelihood, which is recast in a computationally tractable form. We use the corresponding curvature matrices to characterize statistical properties of the recovered parameters. We incorporate in the formalism some of the essential features of the CMB data sets, such as inhomogeneous pixel domain noise, unknown map offsets as well as calibration errors and study their consequences for the separation. We find that the calibration is likely to have a dominant effect on the precision of the spectral parameter determination for a realistic CMB experiment. We apply the algorithm to simulated data and discuss the results. Our focus is on partial sky, total intensity and polarization, CMB experiments such as planned balloon-borne and ground-based efforts, however, the techniques presented here should be also applicable to the full-sky data as for instance, those produced by the Wilkinson Microwave Anisotropy Probe ( WMAP ) satellite and anticipated from the Planck mission.     

The largest scale perturbations: A window on the physics of the beginning

I present results of new statistical techniques for the interpretation of the temperature and polarization maps and power spectra of the cosmic microwave background. We show that the power deficit at low ℓ in the WMAP1 data is consistent with a statistical fluctuation at the 10% level; that future high S/N maps of the temperature and polarization anisotropies can be combined into a reconstruction of the metric perturbations imprinted during inflation; and that machine learning techniques can accelerate cosmological parameter estimation by orders of magnitude while being highly accurate and robust.     

The Sunyaev–Zel'dovich effect contribution to WMAP: a cross-correlation between WMAP and ROSAT

We cross-correlate WMAP and ROSAT diffuse X-ray background maps and look for common features in both data sets. We use the power spectrum of the product maps and the cross-power spectrum to highlight a possible correlation. The power spectrum of the product maps does not detect any correlation and the cross-power spectrum does not show any significant deviation from zero. We explore different explanations for this lack of correlation. A universe with a low value of  σ₈  could naturally explain the lack of correlation. We also discuss the systematic effects that can affect this result, in particular the subtraction of some cluster signal from the ROSAT diffuse maps, which could significantly suppress the correlation signal. These systematic effects considerably reduce the significance of our constraints on the cosmological model. When we include the systematic effects, we find a weaker constraint on  σ₈  , allowing models with values as large as  σ₈= 1  (for  Ω_m= 0.3  ) to be consistent with the lack of correlation. To illustrate the capabilities of the method with future high-quality data, we show how from the correlation signal it should be possible to predict the level of contamination of the Sunyaev–Zel'dovich effect on the power spectrum of the cosmic microwave background. Within the systematic errors, we find evidence that this contribution is negligible for WMAP and is expected to be small in experiments like ACBAR or CBI, but can be important for future high-resolution experiments.     

Understanding the WMAP Cold Spot mystery

The Cold Spot (CS) at galactic coordinates (b = −57°, l = 209°) was discovered in the Wilkinson Microwave Anisotropy Probe (WMAP)data as a cosmic background anomaly. In order to assess the cosmological significance of the Spot, we examine its properties using the cluster analysis of the local extrema in the cosmic microwave background (CMB) signal. We also check the hypothesis that the CMB signal has a non-Gaussian tail, localized in the low-multipole components. We constructed a linear filter, dividing the signal into two parts: non-Gaussian and Gaussian. Using the filter scale as a variable, we can maximize the skewness and kurtosis of the smoothed signal and minimize these statistics. We discovered that the shape of the CS is formed primarily by the components of the CMB signal represented by the multipoles between 10 ≤ ℓ ≤ 20, with a corresponding angular scale of about 5°–10°. This signal leads to the modulation of the CMB on the whole sky, clearly seen at |b| > 30° in both the ILC andWCM maps, rather than in a single localized feature. After subtraction of this modulation, the remaining part of the CMB signal appears to be consistent with statistical homogeneity and Gaussianity. We therefore infer that the mystery of the WMAP Cold Spot reflects directly the peculiarities of low multipoles of the CMB signal, rather than a single local (isolated) defect or the manifestations of a globally anisotropic cosmology.     

A comparison of anisotropic statistical properties of CMB maps based on the WMAP and planck space mission data

We compare the anisotropic properties of the cosmic microwave background (CMB) maps constructed based on the data of NASA’s WMAP (9th year of observations) and ESA’s Planck (2015 release) space missions. In our analysis, we use two two-dimensional estimators of the scatter of the signal on a sphere, which amount to algorithms of mapping the ratio of the scatter in the Northern and Southern hemispheres depending on the method of dividing (specifically, rotating and cutting) the sky into hemispheres. The scatter is computed either as a standard deviation σ, or as the difference between the minimum and maximum values on a given hemisphere. Applying both estimators to the CMB anisotropy datameasured by two spacemissions, Planck and WMAP, we compared the variations of the background at different angular scales.Maps with a resolution of l ≤ 100 show that the division into regions with different levels of statistical anisotropy lies close to the ecliptic plane, and after preliminary removal of the l ≤ 20 harmonics from the CMB data, the anisotropic signal related to the Galaxy begins to dominate.     

Statistics of WMAP ILC map temperature fluctuations towards distant radio galaxies

For 2442 galaxies of the catalog, compiled based on the NED, SDSS, and CATS survey data with redshifts z, > 0.3 we conducted an analysis of the amplitude of temperature fluctuations in the cosmic microwave background (CMB) in the points, corresponding to the direction to these objects. To this end, we used the ILC map from the WMAP mission seven-year data release. We have estimated the dipole component of the background and tested the hypothesis of Kashlinsky on the existence of a “dark bulk flow”, determined for the estimated dipole component of the CMB WMAP by the value of the CMB anisotropy in the direction to the clusters of galaxies. We show that the amplitude of this dipole T _max = 0.012mK is located within the σ interval, estimated by Monte Carlo simulations for the Gaussian fluctuations of the CMB signal in the ΛCDM model. The low amplitude of the dipole indicates that it is impossible to confirm this hypothesis from the WMAP data. In addition, we studied the statistics of the fluctuation amplitude of the microwave signal in the direction to radio galaxies. A weakening of the absolute value of the mean signal in the corresponding fields was discovered.     

Cosmology from 3 years of WMAP CMB data

The combined 3 year observations from the Wilkinson Microwave Anisotropy Probe (WMAP) have yielded full-sky temperature and polarization maps in five frequency bands (K, Ka, Q, V, W) between 23 and 94 GHz. In this article we discuss the cosmological implications of these observations. The combination of temperature and polarization data leads to a significant improvement in the measurement of the reionization optical depth τ = 0.093 ± 0.029. This, in turn, breaks a number of key degeneracies present in the constraints from temperature measurements alone allowing the WMAP CMB data on its own to offer a powerful insight into the universe’s constituents and the processes that generated the initial conditions for structure formation.