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Register a new userA New Probe of Gaussianity and Isotropy applied to the CMB Maps
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We introduce a new mathematical tool (a direction-dependent probe) to analyse the randomness of purported isotropic Gaussian random fields on the sphere. We apply the probe to assess the full-sky cosmic microwave background (CMB) temperature maps produced by the {it Planck} collaboration (PR2 2015 and PR3 2018), with special attention to the inpainted maps. To study the randomness of the fields represented by each map we use the autocorrelation of the sequence of probe coefficients (which are just the full-sky Fourier coefficients $a_{ell,0}$ if the $z$ axis is taken in the probe direction). If the field is {isotropic and Gaussian} then the probe coefficients for a given direction should be realisations of uncorrelated scalar Gaussian random variables. We introduce a particular function on the sphere (called the emph{AC discrepancy}) that accentuates the departure from Gaussianity and isotropy. 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 study the effect of varying the highest multipole used to calculate the AC discrepancy from the initial value of $1500$ to $2500$. In the case of Commander 2015, the AC discrepancy now exhibits antipodal blobs well away from the galactic plane. Finally, we look briefly at the non-inpainted Planck maps, for which the computed AC discrepancy maps have a very different character, with features that are global rather than local. For the particular case of the non-inpainted 2018 texttt{SEVEM} map (which has visible equatorial pollution), we model with partial success the observed behaviour by an isotropic Gaussian random field added to a non-random needlet-like structure located near the galactic centre.
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The leading candidate for the very early universe is described by a period of rapid expansion known as inflation. While the standard paradigm invokes a single slow-rolling field, many different models may be constructed which fit the current observational evidence. In this work we outline theoretical and observational studies of non-Gaussian fluctuations produced by models of inflation and by cosmic strings - topological defects that may be generated in the very early universe during a phase transition. In particular, we consider the imprint of cosmic strings on the cosmic microwave background (CMB) and describe a formalism for the measurement of general four-point correlation functions, or trispectra, using the CMB. In addition we describe the application of our methodology to non-Gaussian signals imprinted in the large scale structure of the universe. Such deviations from Gaussianity are generally expressed in terms of the so-called bispectrum and trispectrum.
We present an upgraded combined estimator, based on Minkowski Functionals and Neural Networks, with excellent performance in detecting primordial non-Gaussianity in simulated maps that also contain a weighted mixture of Galactic contaminations, besides real pixels noise from Planck cosmic microwave background radiation data. We rigorously test the efficiency of our estimator considering several plausible scenarios for residual non-Gaussianities in the foreground-cleaned Planck maps, with the intuition to optimize the training procedure of the Neural Network to discriminate between contaminations with primordial and secondary non-Gaussian signatures. We look for constraints of primordial local non-Gaussianity at large angular scales in the foreground-cleaned Planck maps. For the $mathtt{SMICA}$ map we found ${f}_{rm ,NL} = 33 pm 23$, at $1sigma$ confidence level, in excellent agreement with the WMAP-9yr and Planck results. In addition, for the other three Planck maps we obtain similar constraints with values in the interval ${f}_{rm ,NL} in [33, 41]$, concomitant with the fact that these maps manifest distinct features in reported analyses, like having different pixels noise intensities.
[Abridged] In recent works we have proposed two new large-angle non-Gaussianity indicators based on skewness and kurtosis of patches of CMB sky-sphere, and used them to find out significant deviation from Gaussianity in frequency bands and foreground-reduced CMB maps. Simulated CMB maps with assigned type and amplitude of primordial non-Gaussianity are important tools to determine the strength, sensitivity and limitations of non-Gaussian estimators. Here we investigate whether and to what extent our non-Gaussian indicators have sensitivity to detect non-Gaussianity of local type, particularly with amplitude within the seven-year WMAP bounds. We make a systematic study by employing our statistical tools to generate maps of skewness and kurtosis from several thousands of simulated maps equipped with non-Gaussianity of local type of various amplitudes. We show that our indicators can be used to detect large-angle local-type non-Gaussianity only for relatively large values of the non-linear parameter $f_{rm NL}^{rm local}$. Thus, our indicators have not enough sensitivity to detect deviation from Gaussianity with the non-linear parameter within the seven-year WMAP bounds. This result along with the outcomes of frequency bands and foreground-reduced analyses suggest that non-Gaussianity captured in the previous works by our indicators is not of primordial origin, although it might have a primordial component. We have also made a comparative study of non-Gaussianity of simulated maps and of the full-sky WMAP foreground-reduced seven-year ILC-7yr map. An outcome of this analysis is that the level of non-Gaussianity of ILC-7yr map is higher than that of the simulated maps for $f_{rm NL}^{rm local}$ within WMAP bounds. This provides quantitative indications on the suitability of the ILC-7yr map as a Gaussian reconstruction of the full-sky CMB.
A detection or nondetection of primordial non-Gaussianity by using the cosmic microwave background radiation (CMB) offers a way of discriminating inflationary scenarios and testing alternative models of the early universe. This has motivated the considerable effort that has recently gone into the study of theoretical features of primordial non-Gaussianity and its detection in CMB data. Among such attempts to detect non-Gaussianity, there is a procedure that is based upon two indicators constructed from the skewness and kurtosis of large-angle patches of CMB maps, which have been proposed and used to study deviation from Gaussianity in the WMAP data. Simulated CMB maps equipped with realistic primordial non-Gaussianity are essential tools to test the viability of non-Gaussian indicators in practice, and also to understand the effect of systematics, foregrounds and other contaminants. In this work we extend and complement the results of our previous works by performing an analysis of non-Gaussianity of the high-angular resolution simulated CMB temperature maps endowed with non-Gaussianity of the local type, for which the level of non-Gaussianity is characterized by the dimensionless parameter $f_{rm NL}^{rm local}$
Statistical isotropy (SI) of Cosmic Microwave Background (CMB) fluctuations is a key observational test to validate the cosmological principle underlying the standard model of cosmology. While a detection of SI violation would have immense cosmological ramification, it is important to recognise their possible origin in systematic effects of observations. WMAP seven year (WMAP-7) release claimed significant deviation from SI in the bipolar spherical harmonic (BipoSH) coefficients $A_{ll}^{20}$ and $A_{l-2l}^{20}$. Here we present the first explicit reproduction of the measurements reported in WMAP-7, confirming that beam systematics alone can completely account for the measured SI violation. The possibility of such a systematic origin was alluded to in WMAP-7 paper itself and other authors but not as explicitly so as to account for it accurately. We simulate CMB maps using the actual WMAP non-circular beams and scanning strategy. Our estimated BipoSH spectra from these maps match the WMAP-7 results very well. It is also evident that only a very careful and adequately detailed modelling, as carried out here, can conclusively establish that the entire signal arises from non-circular beam effect. This is important since cosmic SI violation signals are expected to be subtle and dismissing a large SI violation signal as observational artefact based on simplistic plausibility arguments run the serious risk of throwing the baby out with the bathwater.
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