Full-sky Cosmic Microwave Background Research Articles

Estimation of the Full-sky Power Spectrum between Intermediate and Large Angular Scales from Partial-sky CMB Anisotropies Using an Artificial Neural Network

Reliable extraction of cosmological information from observed cosmic microwave background (CMB) maps may require removal of strongly foreground-contaminated regions from the analysis. In this paper, we employ an artificial neural network (ANN) to predict the full-sky CMB angular power spectrum between intermediate and large angular scales from the partial-sky spectrum obtained from a masked CMB temperature anisotropy map. We use a simple ANN architecture with one hidden layer containing 895 neurons. Using 1.2 × 105 training samples of full-sky and corresponding partial-sky CMB angular power spectra at HEALPix pixel resolution parameter N side = 256, we show that the spectrum predicted by our ANN agrees well with the target spectrum at each realization for the multipole range 2 ≤ l ≤ 512. The predicted spectra are statistically unbiased, and they preserve the cosmic variance accurately. Statistically, the differences between the mean predicted and underlying theoretical spectra are within approximately 3σ. Moreover, the probability densities obtained from predicted angular power spectra agree very well with those obtained from “actual” full-sky CMB angular power spectra for each multipole. Interestingly, our work shows that the significant correlations in input cut-sky spectra due to mode–mode coupling introduced on the partial sky are effectively removed, since the ANN learns the hidden pattern between the partial- and full-sky spectra preserving all of the statistical properties. The excellent agreement of statistical properties between the predicted and the ground truth demonstrates the importance of using artificial intelligence systems in cosmological analysis more widely.

Examining statistical isotropy of CMB low multipoles from Planck PR4 data

Low multipoles (l) in cosmic microwave background (CMB) temperature anisotropies have shown some ‘peculiarities’ when examined since the release of the full sky CMB maps, using a variety of tests. In this paper, we concern ourselves with the very first peculiarities seen in CMB data viz., a breakdown of statistical isotropy in the form of axiality and planarity of these low-l modes, and preferred alignments among them. We scrutinize the latest CMB data from ESA's Planck mission, PR4, to evaluate the current status of these deviations. We employ the Power tensor method which allows an invariant characterization of the distribution of power in a given multipole, and apply it to probe the first sixty multipoles i.e., l=2 to 61. We find that there are significant number of modes that are intrinsically anisotropic with a cumulative probability of 0.3%. However since the planarity study reveals that those modes that are unusually planar are subset of these anisotropic modes, we conclude that they may not be intrinsically planar. The quadrupole is still well aligned with the octopole. Besides, l=3, higher multipoles aligned with quadrupole are found to be insignificant. Interestingly, the collective alignment axis of the first sixty multipoles is found to be broadly closer to the axis of dipole, quadrupole, octopole and other modes aligned with l=2.

A Partial-sky Gibbs ILC Approach for the Estimation of CMB Posterior over Large Angular Scales of the Sky

In this article we present a formalism for incorporating the partial-sky maps into the Gibbs ILC algorithm to estimate the joint posterior density of the cosmic microwave background (CMB) signal and the theoretical CMB angular power spectrum given the observed CMB maps. In order to generate the partial-sky maps, we mask all the observed CMB maps provided by the WMAP and Planck satellite full-sky mission using a mask that removes 22% of the entire sky. The mask we use is based on the strength of the thermal dust emissions in the Planck 353 GHz map. While implementing the Gibbs ILC method on the partial-sky maps, we convert the partial-sky-cleaned angular power spectrum into the full-sky angular power spectrum using the mode-mode coupling matrix estimated from the smoothed mask. The main products of our analysis are a partial-sky cleaned best-fit CMB map and an estimate of the underlying full-sky theoretical CMB angular power spectrum in the multipole range 2 ≤ ℓ ≤ 32 along with their error estimates. We validate the method by performing detailed Monte Carlo simulations after using realistic models of foregrounds and detector noise consistent with the WMAP and Planck frequency channels used in our analysis. We can estimate the posterior density and full-sky theoretical CMB angular power spectrum without any need to explicitly model the foreground components from partial-sky maps using our method. Another important feature of this method is that the power spectrum results along with the error estimates can be directly used for cosmological parameter estimations.

An unbiased estimator of the full-sky CMB angular power spectrum at large scales using neural networks

ABSTRACT Accurate estimation of the cosmic microwave background (CMB) angular power spectrum is enticing due to the prospect for precision cosmology it presents. Galactic foreground emissions, however, contaminate the CMB signal and need to be subtracted reliably in order to lessen systematic errors on the CMB temperature estimates. Typically, bright foregrounds in a region lead to further uncertainty in temperature estimates in the area even after some foreground removal technique is performed and hence determining the underlying full-sky angular power spectrum poses a challenge. We explore the feasibility of utilizing artificial neural networks to predict the angular power spectrum of the full-sky CMB temperature maps from the observed angular power spectrum of the partial sky in which CMB temperatures in some bright foreground regions are masked. We present our analysis at large angular scales with two different masks. We produce unbiased predictions of the full-sky angular power spectrum and recover the underlying theoretical power spectrum using neural networks. Our predictions are also uncorrelated to a large extent. We further show that the multipole-space covariances of the predictions of full-sky spectra made by the artificial neural networks are much smaller than those of the estimates obtained using the pseudo-Cℓ method.

Constraints on Cosmological Parameters from the 500 deg2 SPTPOL Lensing Power Spectrum

Abstract We present cosmological constraints based on the cosmic microwave background (CMB) lensing potential power spectrum measurement from the recent 500 deg2 SPTpol survey, the most precise CMB lensing measurement from the ground to date. We fit a flat ΛCDM model to the reconstructed lensing power spectrum alone and in addition with other data sets: baryon acoustic oscillations (BAO), as well as primary CMB spectra from Planck and SPTpol. The cosmological constraints based on SPTpol and Planck lensing band powers are in good agreement when analyzed alone and in combination with Planck full-sky primary CMB data. With weak priors on the baryon density and other parameters, the SPTpol CMB lensing data alone provide a 4% constraint on . Jointly fitting with BAO data, we find , , and , up to away from the central values preferred by Planck lensing + BAO. However, we recover good agreement between SPTpol and Planck when restricting the analysis to similar scales. We also consider single-parameter extensions to the flat ΛCDM model. The SPTpol lensing spectrum constrains the spatial curvature to be and the sum of the neutrino masses to be eV at 95% C.L. (with Planck primary CMB and BAO data), in good agreement with the Planck lensing results. With the differences in the signal-to-noise ratio of the lensing modes and the angular scales covered in the lensing spectra, this analysis represents an important independent check on the full-sky Planck lensing measurement.

The cosmic microwave background Cold Spot anomaly: the impact of sky masking and the expected contribution from the integrated Sachs–Wolfe effect

Abstract We re-analyse the cosmic microwave background (CMB) Cold Spot (CS) anomaly with particular focus on understanding the bias a mask (contaminated by Galactic and point sources) may introduce. We measure the coldest spot, found by applying the Spherical Mexican Hat Wavelet transform on 100 000 cut-sky (masked) and full-sky CMB simulated maps. The CS itself is barely affected by the mask; we estimate a 94 per cent probability that the CS is the full-sky temperature minimum. However, ∼48 per cent (masked fraction of the mask) of full-sky minima are obscured by the mask. Since the observed minima are slightly hotter than the full-sky ensemble of minima, a cut-sky analysis would have found the CS to be significant at ∼2.2σ with a wavelet angular scale of R = 5°. None the less, comparisons to full-sky minima show the CS significance to be only ∼1.9σ and <2σ for all R. The CS on the last scattering surface may be hotter due to the integrated Sachs–Wolfe effect in the line of sight. However, our simulations show that this is on average only ∼10 per cent (about 10 μK but consistent with zero) of the CS temperature profile. This is consistent with Lambda and cold dark matter reconstructions of this effect based on observed line-of-sight voids.

Rotation of the Cosmic Microwave Background Polarization from Weak Gravitational Lensing

When a cosmic microwave background (CMB) photon travels from the surface of last scatter through spacetime metric perturbations, the polarization vector may rotate about its direction of propagation. This gravitational rotation is distinct from, and occurs in addition to, the lensing deflection of the photon trajectory. This rotation can be sourced by linear vector or tensor metric perturbations and is fully coherent with the curl deflection field. Therefore, lensing corrections to the CMB polarization power spectra as well as the temperature-polarization cross correlations due to nonscalar perturbations are modified. The rotation does not affect lensing by linear scalar perturbations, but needs to be included when calculations go to higher orders. We present complete results for weak lensing of the full-sky CMB power spectra by general linear metric perturbations, taking into account both deflection of the photon trajectory and rotation of the polarization. For the case of lensing by gravitational waves, we show that the B modes induced by the rotation largely cancel those induced by the curl component of deflection.

On the coherence of WMAP and Planck temperature maps

The recent data release of ESA's Planck mission together with earlier Wilkinson Microwave Anisotropy Probe (WMAP) releases provide the first opportunity to compare high-resolution full sky cosmic microwave background (CMB) temperature anisotropy maps. To quantify the coherence of these maps beyond the power spectrum, we introduce Generalized Phases in the sense of SO(3), unit vectors in the 2ℓ + 1 dimensional representation spaces. For an isotropic Gaussian distribution, Generalized Phases point to random directions and if there is non-Gaussianity, they represent most of the non-Gaussian information. The alignment of these unit vectors from two maps can be characterized by their angle, 0° expected for full coherence, and 90° for random vectors. We analyse maps from both missions with the same mask and Nside = 512 resolution, and compare both power spectra and Generalized Phases. We find excellent agreement of the Generalized Phases of Planck Spectral Matching Independent Component Analysis map with that of the WMAPQ, V, W maps, rejecting the null hypothesis of no correlations at 5σ for ℓ < 700, ℓ < 900 and ℓ < 1100, respectively, except perhaps for ℓ < 10. Using foreground reduced maps for WMAP increases the phase-coherence. The observed coherence angles can be explained with a simple assumption of Gaussianity and a WMAP noise model neglecting Planck noise, except for low-intermediate ℓ values there is a slight, but significant offset, depending on the WMAP band. On the same scales WMAP power spectrum is about 2.6 per cent higher at a very high significance, while at higher ℓ ranges there appears to be no significant bias. Using our theoretical tools, we predict the phase alignment of Planck with a hypothetical perfect noiseless CMB experiment, finding decoherence at ℓ ≃ 2900; below this value Planck can be used most efficiently to constrain non-Gaussianity.

All sky CMB map from cosmic strings integrated Sachs-Wolfe effect

By actively distorting the cosmic microwave background (CMB) over our past light cone, cosmic strings are unavoidable sources of non-Gaussianity. Developing optimal estimators able to disambiguate a string signal from the primordial type of non-Gaussianity requires calibration over synthetic full sky CMB maps, which until now had been numerically unachievable at the resolution of modern experiments. In this paper, we provide the first high resolution full sky CMB map of the temperature anisotropies induced by a network of cosmic strings since the recombination. The map has about 200 million subarcminute pixels in the healpix format which is the standard in use for CMB analyses (${N}_{\mathrm{side}}=4096$). This premiere required about 800 000 cpu-hours; it has been generated by using a massively parallel ray tracing method piercing through thousands of state of art Nambu-Goto cosmic string numerical simulations which pave the comoving volume between the observer and the last scattering surface. We explicitly show how this map corrects previous results derived in the flat sky approximation, while remaining completely compatible at the smallest scales.

On the optimality of the spherical Mexican hat wavelet estimator for the primordial non-Gaussianity

We study the spherical Mexican hat wavelet (SMHW) as a detector of primordial non-Gaussianity of the local type on the Cosmic Microwave Background (CMB) anisotropies. For this purpose we define third order statistics based on the wavelet coefficient maps and the original map. We find the dependence of these statistics in terms of the non-linear coupling parameter fnl and the bispectrum of this type of non-Gaussianity. We compare the analytical values for these statistics with the results obtained with non-Gaussian simulations for an ideal full-sky CMB experiment without noise. We study the power of this method to detect fnl, i. e. the variance of this parameter, and compare it with the variance obtained from the primary bispectrum for the same experiment. Finally we apply our wavelet based estimator on WMAP-like maps with incomplete sky and inhomogeneous noise and compare with the optimal bispectrum estimator. The results show that the wavelet cubic statistics are as efficient as the bispectrum as optimal detectors of this type of primordial non-Gaussianity.

A full sky, low foreground, high resolution CMB map from WMAP

Context. The WMAP satellite has made available high quality maps of the sky in five frequency bands ranging from 22 to 94 GHz, with the main scientific objective of studying the anisotropies of the Cosmic Microwave Background (CMB). These maps, however, contain a mixture of emission from various astrophysical origin, superimposed on CMB emission.Aims. The objective of the present work is to make a high resolution CMB map in which contamination by such galactic and extra-galactic foreground emissions, as well as by instrumental noise, is as low as possible.Methods. The method used is an implementation of a constrained linear combination of the channels with minimum error variance, and of Wiener filtering, on a frame of spherical wavelets called needlets, allowing localised filtering in both pixel space and harmonic space.Results. We obtain a low contamination low noise CMB map at the resolution of the WMAP W channel, which can be used for a range of scientific studies. We obtain also a Wiener-filtered version with minimal integrated error.Conclusions. The resulting CMB maps offer significantly better rejection of galactic foreground than previous CMB maps from WMAP data. They can be considered as the most precise full-sky CMB temperature maps to date.

Cosmological Applications of a Wavelet Analysis on the Sphere

The cosmic microwave background (CMB) is a relic radiation of the Big Bang and as such it contains a wealth of cosmological information. Statistical analyses of the CMB, in conjunction with other cosmological observables, represent some of the most powerful techniques available to cosmologists for placing strong constraints on the cosmological parameters that describe the origin, content and evolution of the Universe. The last decade has witnessed the introduction of wavelet analyses in cosmology and, in particular, their application to the CMB. We review here spherical wavelet analyses of the CMB that test the standard cosmological concordance model. The assumption that the temperature anisotropies of the CMB are a realisation of a statistically isotropic Gaussian random field on the sphere is questioned. Deviations from both statistical isotropy and Gaussianity are detected in the reviewed works, suggesting more exotic cosmological models may be required to explain our Universe. We also review spherical wavelet analyses that independently provide evidence for dark energy, an exotic component of our Universe of which we know very little currently. The effectiveness of accounting correctly for the geometry of the sphere in the wavelet analysis of full-sky CMB data is demonstrated by the highly significant detections of physical processes and effects that are made in these reviewed works.

Cosmological constraints in the presence of ionizing and resonance radiation at recombination

With the recent measurement of full sky cosmic microwave background (CMB) polarization from WMAP, key cosmological degeneracies have been broken, allowing tighter constraints to be placed on cosmological parameters inferred assuming a standard recombination scenario. Here we consider the effect on cosmological constraints if additional ionizing and resonance radiation sources are present at recombination. We find that the new CMB data significantly improve the constraints on the additional radiation sources, with ${log}_{10}[{ϵ}_{\ensuremath{\alpha}}]&lt;\ensuremath{-}0.5$ and ${log}_{10}[{ϵ}_{i}]&lt;\ensuremath{-}2.4$ at 95% c.l. for resonance and ionizing sources, respectively. Including the generalized recombination scenario, however, we find that the constraints on the scalar spectral index ${n}_{s}$ are weakened to ${n}_{s}=0.98\ifmmode\pm\else\textpm\fi{}0.03$, with the ${n}_{s}=1$ case now well inside the 95% c.l. The relaxation of constraints on tensor modes, scale invariance, dark energy and neutrino masses are also discussed.

On the cosmic microwave background large-scale angular correlations

We study the large-scale angular correlation signatures of the Cosmic Microwave Background (CMB) temperature fluctuations from WMAP data in several spherical cap regions of the celestial sphere, outside the Kp0 or Kp2 cut-sky masks. We applied a recently proposed method to CMB temperature maps, which permits an accurate analysis of their angular correlations in the celestial sphere through the use of normalized histograms of the number of pairs of such objects with a given angular separation versus their angular separation. The method allows for a better comparison of the results from observational data with the expected CMB angular correlations of a statistically isotropic Universe, computed from Monte Carlo maps according to the WMAP best-fit Lambda CDM model. We found that the, already known, anomalous lack of large-scale power in full-sky CMB maps are mainly due to missing angular correlations of quadrupole-like signature. This result is robust with respect to frequency CMB maps and cut-sky masks. Moreover, we also confirm previous results regarding the unevenly distribution in the sky of the large-scale power of WMAP data. In a bin-to-bin correlations analyses, measured by the full covariance matrix chi^2 statistic, we found that the angular correlations signatures in opposite Galactic hemispheres are anomalous at the 98%-99% confidence level.

Cosmic microwave background temperature and polarization pseudo-Cℓestimators and covariances

We develop the pseudo-Cl method for reconstructing the cosmic microwave background (CMB) temperature and polarization auto- and cross-power spectra, and estimate the pseudo-Cl covariance matrix for a realistic experiment on the cut sky. We calculate the full coupling equations for all six possible CMB power spectra, relating the observed pseudo-Cl values to the underlying all-sky Cl values, and test the reconstruction on both full-sky and cut-sky simulated CMB data sets. In particular we consider the reconstruction of the Cl from upcoming ground-based polarization experiments covering areas of a few hundred deg2 and find that the method is fast, unbiased and performs well over a wide range of multipoles from l= 2 to l= 2500. We then calculate the full covariance matrix between the modes of the pseudo-temperature and polarization power spectra, assuming that the underlying CMB fields are Gaussian randomly distributed. The complexity of the covariance matrix prohibits its rapid calculation, required for parameter estimation. Hence we present an approximation for the covariance matrix in terms of convolutions of the underlying power spectra. The coupling matrices in these expressions can be estimated by fitting to numerical simulations, circumventing direct and slow calculation, and further, inaccurate analytic approximations. We show that these coupling matrices are mostly independent of cosmology, and that the full covariance matrix for all six pseudo-Cl power spectra can be quickly and accurately calculated for any given cosmological model using this method. We compare these semi-analytic covariance matrices against simulations and find good agreement, the accuracy of which depends mainly on survey area and the range of cosmological parameters considered.

Statistical Isotropy of the Wilkinson Microwave Anisotropy Probe Data: A Bipolar Power Spectrum Analysis

The statistical expectation values of the temperature fluctuations of the Cosmic Microwave Background (CMB) are assumed to be preserved under rotations of the sky. We investigate the Statistical Isotropy (SI) of the CMB anisotropy maps recently measured by the Wilkinson Microwave Anisotropy Probe (WMAP) using Bipolar Power Spectrum (BiPS) proposed in [Hajian & Souradeep 2003]. The method can probe specific regions in multipole space using appropriate window functions. The BiPS is estimated for full sky CMB anisotropy maps based on the first year WMAP data using a range of window functions. The BiPS spectra computed for both full sky maps for all our window functions are consistent with zero, roughly within $2 \sigma$. The null BiPS results may be interpreted as an absence of strong violation of statistical isotropy in the first-year WMAP data on angular scales larger than that corresponding to $l\sim60$. However, pending a careful direct comparison, our results do not necessarily conflict with the specific SI related anomalies reported using other statistical tests.

HarmonicE/Bdecomposition for CMB polarization maps

The full sky cosmic microwave background polarization field can be decomposed into ``electric'' (E) and ``magnetic'' (B) components that are signatures of distinct physical processes. We give a general construction that achieves separation of E and B modes on arbitrary sections of the sky at the expense of increasing the noise. When E modes are present on all scales the separation of all of the B signal is no longer possible: there are inevitably ambiguous modes that cannot be separated. We discuss the practicality of performing $E/B$ decomposition on large scales with realistic nonsymmetric sky cuts, and show that separation on large scales is possible by retaining only the well supported modes. The large scale modes potentially contain a great deal of useful information, and $E/B$ separation at the level of the map is essential for clean detection of B without confusion from cosmic variance due to the E signal. We give simple matrix manipulations for creating pure E and B maps of the large scale signal for general sky cuts. We demonstrate that the method works well in a realistic case and give estimates of the performance with data from the Planck satellite. In the Appendix we discuss the simple analytic case of an azimuthally symmetric cut, and show that exact $E/B$ separation is possible on an azimuthally symmetric cut with a finite number of nonintersecting circular cuts around foreground sources.

Testing for non-Gaussianity of the cosmic microwave background in harmonic space: An empirical process approach

We present a new, model-independent approach for measuring non-Gaussianity of the cosmic microwave background (CMB) anisotropy pattern. Our approach is based on the empirical distribution function of the normalized spherical harmonic expansion coefficients ${a}_{\mathcal{l}m}$ of a nearly full-sky CMB map, like the ones expected from forthcoming satellite experiments. Using a set of Kolmogorov-Smirnov type tests, we check for Gaussianity and independency of the ${a}_{\mathcal{l}m}.$ We test the method on two non-Gaussian toy models of the CMB, one generated in spherical harmonic space and one in pixel (real) space. We also provide some rigorous results, possibly of independent interest, on the exact distribution of the spherical harmonic coefficients normalized by an estimated angular power spectrum.

Analysis of CMB polarization on an incomplete sky

The full sky cosmic microwave background polarization field can be decomposed into ``electric'' and ``magnetic'' components. Working in harmonic space we construct window functions that allow clean separation of the electric and magnetic modes from observations over only a portion of the sky. We explicitly demonstrate the method for azimuthally symmetric patches, but also present it in a form in principle applicable to arbitrarily shaped patches. From the window functions we obtain variables that allow for robust estimation of the magnetic component without risk of contamination from the probably much larger electric signal. The variables have a very simple noise properties, and further analysis using them should be no harder than analyzing the temperature field. For an azimuthally symmetric patch, such as that obtained from survey missions when the galactic region is removed, the exactly separated variables are fast to compute. We estimate the magnetic signal that could be detected by the Planck satellite in the absence of extra-galactic foregrounds. We also discuss the sensitivity of future experiments to tensor modes in the presence of a magnetic signal generated by weak lensing, and give lossless methods for analyzing the electric polarization field in the case that the magnetic component is negligible. A series of Appendixes review the spin weight formalism and give recursion relations for fast computation of the spin-weighted spherical harmonics and their inner products over azimuthally symmetric patches of the sphere. A further Appendix discusses the statistics of weak signal detection.

Galactic Emission at 19 GH[CLC]z[/CLC

We cross-correlate a 19 GHz full sky Cosmic Microwave Background (CMB) survey with other maps to quantify the foreground contribution. Correlations are detected with the Diffuse Infrared Background Experiment (DIRBE) 240, 140 and 100 micron maps at high latitudes (|b|>30degrees), and marginal correlations are detected with the Haslam 408 MHz and the Reich & Reich 1420 MHz synchrotron maps. The former agree well with extrapolations from higher frequencies probed by the COBE DMR and Saskatoon experiments and are consistent with both free-free and rotating dust grain emission.