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 TOPOLOGY OF THE COSMIC MICROWAVE BACKGROUND ANISOTROPY ON THE SCALE ~1°

1996 ◽  
Vol 05 (04) ◽  
pp. 319-362 ◽  
Author(s):  
D.I. NOVIKOV ◽  
H.E. JØRGENSEN
Keyword(s):  
Cosmic Microwave Background ◽  
Random Field ◽  
Gaussian Noise ◽  
Gaussian Random Field ◽  
Cosmological Models ◽  
Topological Method ◽  
Microwave Background ◽  
Cosmic Microwave Background Anisotropy ◽  
Non Gaussian

In this paper we develop the theory of clusterization of peaks in a Gaussian random field. We have obtained new mathematical results from this theory and the theory of percolation and have proposed a topological method of analysis of sky maps based on these results. We have simulated 10°×10° sky maps of the cosmic microwave background anisotropy expected from different cosmological models with 0.5°–1° resolution in order to demonstrate how this method can be used for detection of non-Gaussian noise in the maps and detection of the Doppler-peak in the spectrum of perturbation of ΔT/T.

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 COSMIC COVARIANCE AND THE LOW QUADRUPOLE ANISOTROPY IN THE WMAP DATA

2008 ◽  
Vol 23 (17n20) ◽  
pp. 1489-1497 ◽  
Author(s):  
LUNG-YIH CHIANG ◽  
PAVEL D. NASELSKY ◽  
PETER COLES
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
A Priori ◽  
Gaussian Random Field ◽  
Minimum Variance ◽  
Microwave Background ◽  
Data Release ◽  
Intrinsic Correlation ◽  
Wmap Data ◽  
Cmb Temperature

Low quadrupole power in the cosmic microwave background (CMB) temperature anisotropies has been a puzzle since WMAP data release. In this talk I will demonstrate that the minimum variance optimization (MVO), a methodology used by many authors including the WMAP science team to separate the CMB from foreground contamination, serves not only to extract the CMB, but to subtract the “cosmic covariance”, an intrinsic correlation between the CMB and the foregrounds. Such subtraction induces low variance in the signal via MVO, which in turn propagates into the multipoles, causing a quadrupole deficit with more than 90% CL. As we do not know the CMB and the foregrounds a priori, and their correlation is subtracted by the MVO in any case, there is therefore an unknown error in the quadrupole power even before the cosmic variance interpretation. We combine the MVO and Monte Carlo simulations, assuming CMB is a Gaussian random field, and the estimated quadrupole power falls in [308.13, 401.97] μ K 2 (at 1 − σ level).

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 Isotropic non-Gaussian gNL-like toy models that reproduce cosmic microwave background anomalies

2019 ◽  
Vol 626 ◽  
pp. A13 ◽  
Author(s):  
F. K. Hansen ◽  
T. Trombetti ◽  
N. Bartolo ◽  
U. Natale ◽  
M. Liguori ◽  
...  
Keyword(s):  
Cosmic Microwave Background ◽  
Large Scale ◽  
Statistical Significance ◽  
Common Mechanism ◽  
Small Scale ◽  
Cold Spot ◽  
Microwave Background ◽  
Significance Level ◽  
Non Gaussian ◽  
Cmb Fluctuations

Context. Based on recent observations of the cosmic microwave background (CMB), claims of statistical anomalies in the properties of the CMB fluctuations have been made. Although the statistical significance of the anomalies remains only at the ∼2−3σ significance level, the fact that there are many different anomalies, several of which support a possible deviation from statistical isotropy, has motivated a search for models that provide a common mechanism to generate them. Aims. The goal of this paper is to investigate whether these anomalies could originate from non-Gaussian cosmological models, and to determine what properties these models should have. Methods. We present a simple isotropic, non-Gaussian class of toy models that can reproduce six of the most extensively studied anomalies. We compare the presence of anomalies found in simulated maps generated from the toy models and from a standard model with Gaussian fluctuations. Results. We show that the following anomalies, as found in the Planck data, commonly occur in the toy model maps: (1) large-scale hemispherical asymmetry (large-scale dipolar modulation), (2) small-scale hemispherical asymmetry (alignment of the spatial distribution of CMB power over all scales ℓ = [2, 1500]), (3) a strongly non-Gaussian hot or cold spot, (4) a low power spectrum amplitude for ℓ <  30, including specifically (5) a low quadrupole and an unusual alignment between the quadrupole and the octopole, and (6) parity asymmetry of the lowest multipoles. We note that this class of toy model resembles models of primordial non-Gaussianity characterised by strongly scale-dependent gNL-like trispectra.

scholarly journals EARLY UNIVERSE SOURCES FOR CMB NON-GAUSSIANITY

2002 ◽  
Vol 17 (29) ◽  
pp. 4273-4280
Author(s):  
ALEJANDRO GANGUI
Keyword(s):  
Power Spectrum ◽  
Cosmic Microwave Background ◽  
Early Universe ◽  
Microwave Background ◽  
Scale Invariant ◽  
Invariant Model ◽  
Primordial Power Spectrum ◽  
Initial States ◽  
Non Gaussian ◽  
Inflationary Models

In the framework of inflationary models with non-vacuum initial states for cosmological perturbations, we study non-Gaussian signatures on the cosmic microwave background (CMB) radiation produced by a broken-scale-invariant model which incorporates a feature at a privileged scale in the primordial power spectrum.

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