We study the ellipticity of contour lines in the sky maps of the cosmic microwave background (CMB) as well as other measures of elongation. The sensitivity of the elongation on the resolution of the CMB maps which depends on the pixelization and the beam profile of the detector, is investigated. It is shown that the current experimental accuracy does not allow to discriminate between cosmological models which differ in curvature by Delta Omega_tot=0.05. Analytical expressions are given for the case that the statistical properties of the CMB are those of two-dimensional Gaussian random fields.
In this paper we present a power spectrum formalism that combines the full three-dimensional information from the galaxy ellipticity field, with information from the cosmic microwave background (CMB). We include in this approach galaxy cosmic shear and galaxy intrinsic alignments, CMB deflection, CMB temperature and CMB polarisation data; including the inter-datum power spectra between all quantities. We apply this to forecasting cosmological parameter errors for CMB and imaging surveys for Euclid-like, Planck, ACTPoL, and CoRE-like experiments. We show that the additional covariance between t…
The recent paper by Berntsen and Hansen devoted to the analysis of elliptic-ity of anisotropies in CMB maps, distorts some statements of previous studies, misses relevant papers, along with superficial comparison of the results (in part of definitions, the role of noise, angular resolution, model parameters).
We present developing of method of the numerical analysis of polarization in the Gauss--Legendre Sky Pixelization (GLESP) scheme for the CMB maps. This incorporation of the polarization transforms in the pixelization scheme GLESP completes the creation of our new method for the numerical analysis of CMB maps. The comparison of GLESP and HEALPix calculations is done.
In this article we present a formalism to incorporate the partial-sky maps to 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 WMAP and Planck satellite mission using a Gaussian smoothed mask formed on the basis of thermal dust emissions in Planck 353 GHz map. The central galactic region from all the input maps is removed after the application of the smoothed mask. While…
We consider the reconstruction of the CMB lensing potential and its power spectrum of the full sphere in presence of sky-cuts due to point sources and Galactic contaminations. Those two effects are treated separately. Small regions contaminated by point sources are filled in using Gaussian constrained realizations. The Galactic plane is simply masked using an apodized mask before lensing reconstruction. This algorithm recovers the power spectrum of the lensing potential with no significant bias.
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 article, we employ an artificial neural network (ANN) to predict the full sky CMB angular power spectrum between intermediate to large angular scales from the partial sky spectrum obtained from masked CMB temperature anisotropy map. We use a simple ANN architecture with one hidden layer containing $895$ neurons. Using $1.2 \times 10^{5}$ training samples of full sky and corresponding partial sky CMB angul…
The CMB maps obtained by observations always possess domains which have to be masked due to severe uncertainties with respect to the genuine CMB signal. Cosmological analyses ideally use full CMB maps in order to get e.g. the angular power spectrum. There are attempts to reconstruct the masked regions at least at low resolutions, i.e. at large angular scales, before a further analysis follows. In this paper, the quality of the reconstruction is investigated for the ILC (7yr) map as well as for 1000 CMB simulations of the LambdaCDM concordance model. The latter allows an error estimation for th…
We propose a new internal linear combination (ILC) method in the pixel space, applicable on large angular scales of the sky, to estimate a foreground minimized Cosmic Microwave Background (CMB) temperature anisotropy map by incorporating prior knowledge about the theoretical CMB covariance matrix. Usual ILC method in pixel space, on the contrary, does not use any information about the underlying CMB covariance matrix. The new approach complements the usual pixel space ILC technique specifically at low multipole region, using global information available from theoretical CMB covariance matrix a…
In arXiv:1105.1081, Eriksen and Wehus try to criticise the use of Kolmogorov's stochasticity parameter (KSP) for CMB data analysis. Their discussion is based on a serious misunderstanding of the randomness and Arnold's work. Their note includes numerous further inaccuracies and groundless statements. However, this short note is concerned with KSP method only.
We study a strategy to determine miscalibrated polarization angles of cosmic microwave background (CMB) experiments using the observed $EB$ polarization power spectra of CMB and Galactic foreground emission. We apply the methodology of Minami et al.(2019) developed for full-sky observations to ground-based experiments such as Simons Observatory. We take into account the $E$-to-$B$ leakage and $\ell$-to-$\ell$ covariance due to partial sky coverage using the public code NaMaster. We show that our method yields an unbiased estimate of miscalibrated angles. Our method also enables simultaneous de…
Two groups [3,4] have confirmed the results of our paper concerning the actual existence of low variance circles in the cosmic microwave background (CMB) sky. They also point out that the effect does not contradict the LCDM model - a matter which is not in dispute. We point out two discrepancies between their treatment and ours, however, one technical, the other having to do with the very understanding of what constitutes a Gaussian random signal. Both groups simulate maps using the CMB power spectrum for LCDM, while we simulate a pure Gaussian sky plus the WMAP's noise, which points out the c…
We present efficient algorithms for CMB lensing simulation and power spectrum es- timation for flat-sky CMB polarization maps. We build a pure B-mode estimator to remedy E to B leakage due to partial sky coverage. We show that our estimators are unbiased, and consistent with the projected errors. We demonstrate our algorithm using simulated observations of small sky patches with realistic noise and weights for upcoming CMB polarization experiments.
Detailed measurements of the CMB lensing signal are an important scientific goal of ongoing ground-based CMB polarization experiments, which are mapping the CMB at high resolution over small patches of the sky. In this work we simulate CMB polarization lensing reconstruction for the $EE$ and $EB$ quadratic estimators with current-generation noise levels and resolution, and show that without boundary effects the known and expected zeroth and first order $N^{(0)}$ and $N^{(1)}$ biases provide an adequate model for non-signal contributions to the lensing power spectrum estimators. Small sky areas…
We show an efficient way to compute wide-angle or all-sky statistics of galaxy intrinsic alignment in three-dimensional configuration space. For this purpose, we expand the two-point correlation function using a newly introduced spin-dependent tripolar spherical harmonic basis. Therefore, the angular dependences on the two line-of-sight (LOS) directions pointing to each pair of objects, which are degenerate with each other in the conventional analysis under the small-angle or plane-parallel (PP) approximation, are unambiguously decomposed. By means of this, we, for the first time, compute the …
Statistical isotropy (SI) is one of the fundamental assumptions made in cosmological model building. This assumption is now being rigorously tested using the almost full sky measurements of the CMB anisotropies. A major hurdle in any such analysis is to handle the large biases induced due to the process of masking. We have developed a new method of analysis, using the bipolar spherical harmonic basis functions, in which we semi-analytically evaluate the modifications to SI violation induced by the mask. The method developed here is generic and can be potentially used to search for any arbitrar…
We demonstrate the feasibility to generate surrogates by Fourier-based methods for an incomplete data set. This is performed for the case of a CMB analysis, where astrophysical foreground emission, mainly present in the Galactic plane, is a major challenge. The shuffling of the Fourier phases for generating surrogates is now enabled by transforming the spherical harmonics into a new set of basis functions that are orthonormal on the cut sky. The results show that non-Gaussianities and hemispherical asymmetries in the CMB as identified in several former investigations, can still be detected eve…
Multi-frequency observations are needed to separate the CMB from foregrounds and accurately extract cosmological information from the data. The Analytical Blind Separation (ABS) method is dedicated to extracting the CMB power spectrum from multi-frequency observations in the presence of contamination from astrophysical foreground emission and instrumental noise. In this study, we apply the ABS method to simulated sky maps as could be observed with a future space-borne survey, in order to test the method's capability for determining the CMB polarization $E$- and $B$-mode power spectra. We prese…
The presence of astrophysical emissions between the last scattering surface and our vantage point requires us to apply a foreground mask on CMB sky map, leading to large cut around the Galactic equator and numerous holes. Since many CMB analyses, including non-Gaussianity study may be performed on a whole sky map in a more straightforward and reliable manner, it is of utmost importance to develop an efficient method to in-paint the CMB sky map, while still preserving statistical properties. In this letter, we consider Monte-Carlo simulation of constrained Gaussian field and derive it for CMB a…
A persistent signal of power asymmetry on opposite hemispheres of CMB sky was seen in full-sky temperature measurements made so far. This asymmetry was seen in microwave sky from WMAP as well as PLANCK satellites, and calls for attention the larger question of \emph{statistical isotropy}, one of the foundational principles of modern cosmology. In this work we present an analysis of polarized CMB maps from PLANCK 2015 full mission data. We apply the local variance estimator on low resolution $E-$mode maps from PLANCK 2015 polarization \texttt{Commander} solution. We find a significant hemispher…
In a recent paper, Gurzadyan & Penrose claim to have found directions on the sky centred on which are circles of anomalously low variance in the cosmic microwave background (CMB). These features are presented as evidence for a particular picture of the very early Universe. We attempted to repeat the analysis of these authors, and we can indeed confirm that such variations do exist in the temperature variance for annuli around points in the data. However, we find that this variation is entirely expected in a sky which contains the usual CMB anisotropies. In other words, properly simulated Gauss…
y-type spectral distortions of the cosmic microwave background allow us to detect clusters and groups of galaxies, filaments of hot gas and the non-uniformities in the warm hot intergalactic medium. Several CMB experiments (on small areas of sky) and theoretical groups (for full sky) have recently published y-type distortion maps. We propose to search for two artificial hot spots in such y-type maps resulting from the incomplete subtraction of the effect of the motion induced dipole on the cosmic microwave background sky. This dipole introduces, at second order, additional temperature and y-di…
Noticeable deviations from the prediction of the fiducial LCDM cosmology are found in the angular power spectrum of the CMB. Besides large-angle anomalies, the WMAP 1st year data revealed a dip in the power spectrum at l \sim 200, which seemed to disappear in the 3rd year and subsequent angular power spectra. Using the WMAP 1st, 3rd, and 5th year data as well as the 5 year coadded data, we study the intensity and spatial distribution of this feature in order to unveil its origin and its implications for the cosmological parameters. We show that in all WMAP data releases there is a substantial …
Our peculiar motion with respect to the CMB rest frame represents a preferred direction in the observed CMB sky since it induces an apparent deflection of the observed CMB photons (aberration) and a shift in their frequency (Doppler). Both effects distort the multipoles $a_{\ell m}$'s at all $\ell$'s. Such effects are real as it has been recently measured for the first time by Planck according to what was forecast in some recent papers. However, the common lore when estimating a power spectrum from CMB is to consider that Doppler affects only the $\ell=1$ multipole, neglecting any other correc…
We review and compare two different CMB dipole estimators discussed in the literature, and assess their performances through Monte Carlo simulations. The first method amounts to simple template regression with partial sky data, while the second method is an optimal Wiener filter (or Gibbs sampling) implementation. The main difference between the two methods is that the latter approach takes into account correlations with higher-order CMB temperature fluctuations that arise from non-orthogonal spherical harmonics on an incomplete sky, which for recent CMB data sets (such as Planck) is the domin…
The standard model of cosmology predicts a statistically isotropic (SI) CMB sky. However, the SI violation signals are always present in an observed sky-map. Different cosmological artifacts, measurement effects and unavoidable effects during data analysis etc. may lead to isotropy violation in an otherwise SI sky. Therefore, a proper data analysis technique should calculate all these SI violation signals, so that they can be matched with SI violation signals from the known sources and then conclude if there is any intrinsic SI violation in the CMB sky. In one of our recent works, we presented…
We present a new model of the microwave sky in polarization that can be used to simulate data from CMB polarization experiments. We exploit the most recent results from the Planck satellite to provide an accurate description of the diffuse polarized foreground synchrotron and thermal dust emission. Our model can include the two mentioned foregrounds, and also a constructed template of Anomalous Microwave Emission (AME). Several options for the frequency dependence of the foregrounds can be easily selected, to reflect our uncertainties and to test the impact of different assumptions. Small angu…
CMB polarization signal may be decomposed into gradient-like (E) and curl-like (B) mode. We have investigated E/B decomposition in pixel space. We find E/B mixing due to incomplete sky is localized in pixel-space, and negligible in the regions far away from the masked area. By estimating the expected local leakage power, we have diagnosed ambiguous pixels. Our criteria for ambiguous pixels (i.e. r_c) is associated with the tensor-to-scalar ratio of B mode power spectrum, which the leakage power is comparable to. By setting r_c to a lower value, we may reduce leakage level, but reduce sky fract…
The largest fluctuation in the observed CMB temperature field is the dipole, its origin being usually attributed to the Doppler Effect - the Earth's velocity with respect to the CMB rest frame. The lowest order boost correction to temperature multipolar coefficients appears only as a second order correction in the temperature power spectrum, $C_{\ell}$. Since v/c - 10-3, this effect can be safely ignored when estimating cosmological parameters [4-7]. However, by cutting our galaxy from the CMB sky we induce large-angle anisotropies in the data. In this case, the corrections to the cut-sky $C_{…
The angular two-point correlation function of the temperature of the cosmic microwave background (CMB), as inferred from nearly all-sky maps, is very close to zero on large angular scales. A statistic invented to quantify this feature, $S_{1/2}$, has a value sufficiently low that only about 7 in 1000 simulations generated assuming the standard cosmological model have lower values; i.e., it has a $p$-value of 0.007. As such, it is one of several unusual features of the CMB sky on large scales, including the low value of the observed CMB quadrupole, whose importance is unclear: are they multiple…
It is well known that our motion with respect to the cosmic microwave background (CMB) rest frame introduces a large dipolar CMB anisotropy, with an amplitude ~beta=v/c~10^{-3}. In addition it should lead to a small breaking of statistical isotropy which becomes most notable at higher multipoles. In principle this could be used to determine our velocity with respect to the CMB rest frame using high angular resolution data from Planck, without directly relying on the amplitude and direction of the CMB dipole, allowing us to constrain cosmological models in which the cosmic dipole arises partly …
Recent results of the ESA Planck satellite have confirmed the existence of some anomalies in the statistical distribution of the cosmic microwave background (CMB) anisotropies. One of the most intriguing anomalies is the Cold Spot, firstly detected in the WMAP data by Vielva et al. (2004). In a later paper, Vielva et al. (2011) developed a method to probe the anomalous nature of the Cold Spot by using the cross-correlation of temperature and polarization of the CMB fluctuations. Whereas this work was built under the assumption of analysing full-sky data, in the present paper we extend such app…
Mechanisms have been proposed that might rotate the linear polarization of the cosmic microwave background (CMB) as it propagates from the surface of last scatter. In the simplest scenario, the rotation will be uniform across the sky, but the rotation angle may also vary across the sky. We develop in detail the complete set of full-sky quadratic estimators for the rotation of the CMB polarization that can be constructed from the CMB temperature and polarization. We derive the variance with which these estimators can be measured and show that these variances reduce to the simpler flat-sky expre…
A crucial problem for partial sky analysis of CMB polarization is the $E$-$B$ leakage problem. Such leakage arises from the presence of `ambiguous' modes that satisfy properties of both $E$ and $B$ modes. Solving this problem is critical for primordial polarization $B$ mode detection in partial sky CMB polarization experiments. In this work we introduce a new method for reducing the leakage. We demonstrate that if we complement the $E$-mode information outside the observation patch with ancillary data from full-sky CMB observations, we can reduce and even effectively remove the $E$-to-$B$ leak…
We extend the internal template foreground removal method by accounting for spatially varying spectral parameters such as the spectral indices of synchrotron and dust emission and the dust temperature. As the previous algorithm had to assume that the spectral parameters are uniform over the full sky (or some significant fraction of the sky), it resulted in a bias in the tensor-to-scalar ratio parameter $r$ estimated from foreground-cleaned polarization maps of the cosmic microwave background (CMB). The new algorithm, "Delta-map method", accounts for spatially varying spectra to first order in …
Thompson scattering of cosmic microwave background (CMB) photons off of free electrons during the reionization epoch induces a correlation between the distribution of galaxies and the polarization pattern of the CMB, the magnitude of which is proportional to the quadrupole moment of radiation at the time of scattering. Since the quadrupole moment generated by gravitational waves (GWs) gives rise to a different polarization pattern than that produced by scalar modes, one can put interesting constraints on the strength of GWs on large scales by cross-correlating the small scale galaxy distributi…
In this paper we estimate diffuse foreground minimized Cosmic Microwave Background (CMB) Stokes Q and U polarization maps based upon the fundamental concept of Gaussian nature of CMB and strong non-Gaussian nature of astrophysical polarized foregrounds using WMAP nine year published polarization maps. We excise regions of the sky that define position of the known point sources, regions that are strongly contaminated by either the detector noise or by the diffuse foregrounds or both, and then perform foreground minimizations over the surviving sky regions that constitute approximately $50\%$ of…
The existence of concentric low variance circles in the CMB sky, generated by black-hole encounters in an aeon preceding our big bang, is a prediction of the Conformal Cyclic Cosmology. Detection of three families of such circles in WMAP data was recently reported by Gurzadyan & Penrose (2010). We reassess the statistical significance of those circles by comparing with Monte Carlo simulations of the CMB sky with realistic modeling of the anisotropic noise in WMAP data. We find that the circles are not anomalous and that all three groups are consistent at 3sigma level with a Gaussian CMB sky as…
Any isotropy violating phenomena on cosmic microwave background (CMB) induces off-diagonal correlations in the two-point function. These correlations themselves can be used to estimate the underlying anisotropic signals. Masking due to residual foregrounds, or availability of partial sky due to survey limitation, are unavoidable circumstances in CMB studies. But, masking induces additional correlations, and thus complicates the recovery of such signals. In this work, we discuss a procedure based on bipolar spherical harmonic (BipoSH) formalism to comprehensively addresses any spurious correlat…
Rayleigh scattering from neutral hydrogen during and shortly after recombination causes the CMB anisotropies to be significantly frequency dependent at high frequencies. This may be detectable with Planck, and would be a strong signal in any future space-based CMB missions. The later peak of the Rayleigh visibility compared to Thomson scattering gives an increased large-scale CMB polarization signal that is a greater than 4% effect for observed frequencies greater than 500GHz. There is a similar magnitude suppression on small scales from additional damping. Due to strong correlation between th…
We present two novel methods for the estimation of the angular power spectrum of cosmic microwave background (CMB) anisotropies. We assume an absolute CMB experiment with arbitrary asymmetric beams and arbitrary sky coverage. The methods differ from earlier ones in that the power spectrum is estimated directly from time-ordered data, without first compressing the data into a sky map, and they take into account the effect of asymmetric beams. In particular, they correct the beam-induced leakage from temperature to polarization. The methods are applicable to a case where part of the sky has been…
Cosmic Microwave Background (CMB) full-sky temperature data show a hemispherical asymmetry in power nearly aligned with the Ecliptic. In real space, this anomaly can be quantified by the temperature variance in the northern and southern Ecliptic hemispheres. In this context, the northern hemisphere displays an anomalously low variance while the southern hemisphere appears unremarkable (consistent with expectations from the best-fitting theory, $Λ$CDM). While this is a well established result in temperature, the low signal-to-noise ratio in current polarization data prevents a similar compariso…
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…
We analyze the randomness of the sky distribution of cosmic gamma-ray bursts. These events are associated with massive galaxies, spiral or elliptical, and therefore their positions should trace the large-scale structure, which, in turn, could show up in the sky distribution of fluctuations of the cosmic microwave background (CMB). We test this hypothesis by mosaic correlation mapping of the distributions of CMB peaks and burst positions, find the distribution of these two signals to be correlated, and interpret this correlation as a possible systematic effect.
Cosmic microwave background (CMB) lensing is an integrated effect whose kernel is greater than half the peak value in the range $1<z<5$. Measuring this effect offers a powerful tool to probe the large-scale structure of the Universe at high redshifts. With the increasing precision of ongoing CMB surveys, other statistics than the lensing power spectrum, in particular the lensing bi-spectrum, will be measured at high statistical significance. This will provide ways to improve the constraints on cosmological models and lift degeneracies. Following on an earlier paper, we test analytical predicti…
Based on realistic simulations, we propose an hybrid method to reconstruct the lensing potential power spectrum, directly on PLANCK-like CMB frequency maps. It implies using a large galactic mask and dealing with a strong inhomogeneous noise. For l < 100, we show that a full-sky inpainting method, already described in a previous work, still allows a minimal variance reconstruction, with a bias that must be accounted for by a Monte-Carlo method, but that does not couple to the deflection field. For l>100 we develop a method based on tiling the cut-sky with local 10x10 degrees overlapping tangen…
Deviations of the observed cosmic microwave background (CMB) from the standard model, known as "anomalies", are obviously highly significant and deserve to be pursued more aggressively in order to discover the physical phenomena underlying them. Through intensive investigation we have discovered that there are equally surprising features in the digits of the number $π$, and moreover there is a remarkable correspondence between each type of peculiarity in the digits of $π$ and the anomalies in the CMB. Putting aside the unreasonable possibility that these are just the sort of flukes that appear…
We forecast the number of galaxy clusters that can be detected via the thermal Sunyaev-Zeldovich (tSZ) signals by future cosmic microwave background (CMB) experiments, primarily the wide area survey of the CMB-S4 experiment but also CMB-S4's smaller delensing survey and the proposed CMB-HD experiment. We predict that CMB-S4 will detect 75,000 clusters with its wide survey of $f_{\rm sky}$ = 50% and 14,000 clusters with its deep survey of $f_{\rm sky}$ = 3%. Of these, approximately 1350 clusters will be at $z \ge 2$, a regime that is difficult to probe by optical or X-ray surveys. We assume CMB…
From South to North: Leveraging Ground-Based LATs for Full-Sky CMB Delensing and Constraints on $r$
Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences（高能物理研究所粒子天体物理重点实验室）；University of Chinese Academy of Sciences（中国科学院大学）
The lensing convergence measurable with future CMB surveys like CMB-S4 will be highly correlated with the clustering observed by deep photometric large scale structure (LSS) surveys such as the LSST, with cross-correlation coefficient as high as 95\%. This will enable use of sample variance cancellation techniques to determine cosmological parameters, and use of cross-correlation measurements to break parameter degeneracies. Assuming large sky overlap between CMB-S4 and LSST, we show that a joint analysis of CMB-S4 lensing and LSST clustering can yield very tight constraints on the matter ampl…
We develop optimised estimators of two sorts of power spectra for fields defined on the sky, in the presence of partial sky coverage. The first is the cross-power spectrum of two fields on the sky; the second is the skew spectrum of three fields. These can probe the Integrated Sachs Wolfe Effect (ISW) at large angular scales and the Sunyaev Zéldovich (SZ) effect from hot gas in clusters at small angular scales. The skew spectrum, recently introduced by Munshi & Heavens (2009), is an optimised statistic which can be tuned to study a particular form of non-Gaussianity, such as may arise in the e…
The direct evaluation of manifestly optimal, cut-sky CMB power spectrum and bispectrum estimators is numerically very costly, due to the presence of inverse-covariance filtering operations. This justifies the investigation of alternative approaches. In this work, we mostly focus on an inpainting algorithm that was introduced in recent CMB analyses to cure cut-sky suboptimalities of bispectrum estimators. First, we show that inpainting can equally be applied to the problem of unbiased estimation of power spectra. We then compare the performance of a novel inpainted CMB temperature power spectru…
