A new probe of Gaussianity and isotropy with application to cosmic microwave background maps

2021 ◽  
pp. 2150084
Author(s):  
J. Hamann ◽  
Q. T. Le Gia ◽  
I. H. Sloan ◽  
Y. G. Wang ◽  
R. S. Womersley
Keyword(s):  
Cosmic Microwave Background ◽  
Random Fields ◽  
Fourier Coefficients ◽  
Galactic Plane ◽  
Gaussian Random Fields ◽  
Mathematical Tool ◽  
Microwave Background ◽  
Temperature Maps ◽  
Cmb Temperature ◽  
Dependent Probe

We introduce a new mathematical tool (a direction-dependent probe) to analyze the randomness of purported isotropic Gaussian random fields on the sphere. If the field is isotropic and Gaussian then the probe coefficients for a given direction should be realizations of uncorrelated scalar Gaussian random variables. To study the randomness of a field, we use the autocorrelation of the sequence of probe coefficients (which are just the Fourier coefficients [Formula: see text] if the [Formula: see text]-axis is taken in the probe direction). We introduce a particular function on the sphere (called the AC discrepancy) that accentuates the departure from Gaussianity and isotropy. We apply the probe to assess the full-sky cosmic microwave background (CMB) temperature maps produced by the Planck collaboration (PR2 2015 and PR3 2018), with special attention to the inpainted maps. We find that for some of the maps, there are many directions for which the departures are significant, especially near the galactic plane. We also look briefly at the noninpainted Planck maps, for which the computed AC discrepancy maps have a very different character, with features that are global rather than local.

scholarly journals ELLIPTICITY OF STRUCTURES IN CMB SKY MAPS

2011 ◽  
Vol 20 (11) ◽  
pp. 2253-2280 ◽  
Author(s):  
RALF AURICH ◽  
HOLGER S. JANZER ◽  
SVEN LUSTIG ◽  
FRANK STEINER
Keyword(s):  
Cosmic Microwave Background ◽  
Random Fields ◽  
Gaussian Random Fields ◽  
Beam Profile ◽  
Statistical Properties ◽  
Two Dimensional ◽  
Microwave Background ◽  
Experimental Accuracy ◽  
Contour Lines ◽  
Analytical Expressions

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 one to discriminate between cosmological models which differ in curvature by ΔΩ 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.

scholarly journals Investigating non-Gaussianity in Cosmic Microwave Background temperature maps using spherical harmonic phases

2022 ◽  
Vol 2022 (01) ◽  
pp. 001
Author(s):  
Sarvesh Kumar Yadav ◽  
Rajib Saha
Keyword(s):  
Cosmic Microwave Background ◽  
Spherical Harmonic ◽  
Gaussian Random Field ◽  
Random Sets ◽  
Accurate Estimation ◽  
Implicit Assumption ◽  
Microwave Background ◽  
Non Gaussian ◽  
Temperature Maps ◽  
Cmb Temperature

Abstract In the era of precision cosmology, accurate estimation of cosmological parameters is based upon the implicit assumption of the Gaussian nature of Cosmic Microwave Background (CMB) radiation. Therefore, an important scientific question to ask is whether the observed CMB map is consistent with Gaussian prediction. In this work, we extend previous studies based on CMB spherical harmonic phases (SHP) to examine the validity of the hypothesis that the temperature field of the CMB is consistent with a Gaussian random field (GRF). The null hypothesis is that the corresponding CMB SHP are independent and identically distributed in terms of a uniform distribution in the interval [0, 2π] [1,2]. We devise a new model-independent method where we use ordered and non-parametric Rao's statistic, based on sample arc-lengths to comprehensively test uniformity and independence of SHP for a given ℓ mode and independence of nearby ℓ mode SHP. We performed our analysis on the scales limited by spherical harmonic modes ≤ 128, to restrict ourselves to signal-dominated regions. To find the non-uniform or dependent sets of SHP, we calculate the statistic for the data and 10000 Monte Carlo simulated uniformly random sets of SHP and use 0.05 and 0.001 α levels to distinguish between statistically significant and highly significant detections. We first establish the performance of our method using simulated Gaussian, non-Gaussian CMB temperature maps, along with observed non-Gaussian 100 and 143 GHz Planck channel maps. We find that our method, performs efficiently and accurately in detecting phase correlations generated in all of the non-Gaussian simulations and observed foreground contaminated 100 and 143 GHz Planck channel temperature maps. We apply our method on Planck satellite mission's final released CMB temperature anisotropy maps- COMMANDER, SMICA, NILC, and SEVEM along with WMAP 9 year released ILC map. We report that SHP corresponding to some of the m-modes are non-uniform, some of the ℓ mode SHP and neighboring mode pair SHP are correlated in cleaned CMB maps. The detection of non-uniformity or correlation in the SHP indicates the presence of non-Gaussian signals in the foreground minimized CMB maps.

scholarly journals The Impact of CN Line Profile Measurements on the Cosmic Microwave Background Temperature

1990 ◽  
Vol 139 ◽  
pp. 390-391
Author(s):  
M. E. Kaiser ◽  
E. L. Wright
Keyword(s):  
Cosmic Microwave Background ◽  
Line Profile ◽  
Line Of Sight ◽  
High Signal ◽  
Microwave Background ◽  
A Value ◽  
Cosmic Microwave Background Temperature ◽  
Background Temperature ◽  
The Impact ◽  
Cmb Temperature

We present moderate to high signal-to-noise high-resolution (R ≈ 150,000–170,000) optical spectra toward ζ Oph. Gaussian fits to our data indicate a value of the line-width parameter b, of b = 1.4 ± 0.2 km s−1, along this line of sight. When CN is used as an indirect probe of the cosmic microwave background (CMB) temperature, the line profile is used to determine saturation corrections in the line. This affects column density calculations, which are reflected in the excitation temperature. Current measurements of the b-value along this line of sight range from 0.88 ± 0.02 km s−1 (Crane et al. 1986) to 1.3 ± 0.1 km s−1 (Hegyi, Traub, and Carleton 1972). The extreme range of these b-values yield saturation corrections to the CMB temperature that differ by 0.05 K, which is equal to the quoted precision of current measurements. Preliminary analysis of observations toward HD 29647 indicate that TCMB = 2.70 ± 0.14 K at 2.64 mm toward this line of sight.

scholarly journals Clustering of hotspots in the cosmic microwave background

2019 ◽  
Vol 206 ◽  
pp. 09017
Author(s):  
En Zuo Joel Low ◽  
Abel Yang
Keyword(s):  
Cosmic Microwave Background ◽  
Galaxy Formation ◽  
Equilibrium Distribution ◽  
Negative Binomial ◽  
Clustering Algorithms ◽  
Quasi Equilibrium ◽  
Microwave Background ◽  
Temperature Maps ◽  
Recombination Epoch ◽  
Frequency Temperature

The physics behind the origin and composition of the Cosmic Microwave Background (CMB) is a well-established topic in the field of Cosmology. Literature on CMB anisotropies reveal consistency with Gaussianity [1], but these were conducted on full multi-frequency temperature maps. In this thesis, we utilise clustering algorithms to specifically conduct statistical analyses on the distribution of hotspots in the CMB. We describe a series of data processing and clustering methodologies conducted, with results that conclusively show that the counts-in-cells distribution of hotspots in the CMB does not follow a Poisson distribution. Rather, the distribution exhibits a much closer fit to both the Negative Binomial Distribution (NBD) and the Gravitational Quasi-Equilibrium Distribution (GQED). From this result, we conclude that structure likely existed in the early universe, from the period of the recombination Epoch, possibly opening new insights in the field of galaxy formation.

scholarly journals RÉNYI FUNCTION FOR MULTIFRACTAL RANDOM FIELDS

Fractals ◽  
2013 ◽  
Vol 21 (02) ◽  
pp. 1350009 ◽  
Author(s):  
NIKOLAI N. LEONENKO ◽  
NARN-RUEIH SHIEH
Keyword(s):  
Cosmic Microwave Background ◽  
Spherical Harmonics ◽  
Random Fields ◽  
Background Radiation ◽  
Microwave Background ◽  
Basic Scheme ◽  
Infinite Products ◽  
Microwave Background Radiation ◽  
Log Normal ◽  
Isotropic Random

This paper presents the basic scheme and the log-normal, log-gamma and log-negative-inverted-gamma scenarios to establish the Rényi function for infinite products of homogeneous isotropic random fields on Rn; in particular for random fields on the sphere in R3. The motivation of this paper is the test of (non-)Gaussianity on the Cosmic Microwave Background Radiation (CMBR) in Cosmology. In the presentation, we need to employ spherical harmonics for some concrete computations.

SYMMETRIES OF THE GALACTIC FOREGROUNDS IN THE WMAP DATA

2005 ◽  
Vol 14 (10) ◽  
pp. 1769-1778 ◽  
Author(s):  
PAVEL D. NASELSKY ◽  
IGOR D. NOVIKOV
Keyword(s):  
Cosmic Microwave Background ◽  
Coordinate System ◽  
Spherical Harmonics ◽  
Galactic Plane ◽  
Polar Coordinate System ◽  
Microwave Background ◽  
The Galaxy ◽  
Polar Coordinate ◽  
Wmap Data

We present a specific periodicity of the Galaxy images in the multipole domain which can be used to separate the cosmic microwave background (CMB) signal from the Galaxy and foreground component. This method takes into consideration all the coefficients of the expansion of the signal from the sky ΔT(Θ,ϕ) into spherical harmonics and dealing with combination of multipoles al,m and al+Δ,m for each multipole mode (ℓ, -ℓ ≤ m ≤ ℓ) from the whole sky without galactic cut, masks or any dissection of the whole sky into disjoint regions. For the polar coordinate system we use particular values for Δ = 4n, n = 1, 2,… which remove all bright pointlike sources that are localized in the Galactic plane and strong diffused component down to the CMB level. To illustrate the significant correlations of the pointlike sources and the foregrounds al,m, al+Δ,m coefficients we apply this method to the WMAP Q, V and W bands in order to remove these marks of the Galaxy from the maps. We believe that our method would be useful for separating the CMB signal from different kind of "noises" in the maps.

scholarly journals On the detection of point sources in Planck LFI 70 GHz CMB maps based on cleaned K-map

2015 ◽  
Vol 30 (14) ◽  
pp. 1550083
Author(s):  
H. G. Khachatryan ◽  
A. L. Kashin ◽  
E. Poghosyan ◽  
G. Yegoryan
Keyword(s):  
Cosmic Microwave Background ◽  
Point Source ◽  
Temperature Data ◽  
Point Sources ◽  
Detection Technique ◽  
Source Detection ◽  
Microwave Background ◽  
Probe Point ◽  
Cmb Temperature ◽  
Planck Satellite

We use the Planck LFI 70 GHz data to further probe point source detection technique in the sky maps of the cosmic microwave background (CMB) radiation. The method developed by Tegmark et al. for foreground reduced maps and the Kolmogorov parameter as the descriptor are adopted for the analysis of Planck satellite CMB temperature data. Most of the detected points coincide with point sources already revealed by other methods. However, we have also found nine source candidates for which still no counterparts are known.

scholarly journals A pixel space method for testing dipole modulation in the CMB polarization

2020 ◽  
Vol 492 (3) ◽  
pp. 3994-4004
Author(s):  
Shamik Ghosh ◽  
Pankaj Jain
Keyword(s):  
Cosmic Microwave Background ◽  
Focal Plane ◽  
Microwave Background ◽  
Power Asymmetry ◽  
Planck Data ◽  
Real Effect ◽  
Cmb Polarization ◽  
Dipole Modulation ◽  
Space Method ◽  
Cmb Temperature

ABSTRACT We introduce a pixel space method to detect dipole modulation or hemispherical power asymmetry in the cosmic microwave background (CMB) polarization. The method relies on the use of squared total polarized flux whose ensemble average picks up a dipole due to the dipole modulation in the CMB polarization. The method is useful since it can be easily applied to partial sky. We define several statistics to characterize the amplitude of the detected signal. Through simulations, we show that the method can be used to reliably extract the signal at a 2.7σ level or higher in future CORE-like missions, assuming that the signal is present in the CMB polarization at the level detected by the Planck mission in the CMB temperature. An application of the method to the 2018 Planck data does not detect a significant effect, when taking into account the presence of correlated detector noise and residual systematics in the data. Using the Full Focal Plane 10, we find the presence of a very strong bias that might be masking any real effect.

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