Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userGeometrical estimators as a test of Gaussianity in the CMB
74
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We investigate the power of geometrical estimators on detecting non-Gaussianity in the cosmic microwave background. In particular the number, eccentricity and Gaussian curvature of excursion sets above (and below) a threshold are studied. We compare their different performance when applied to non-Gaussian simulated maps of small patches of the sky, which take into account the angular resolution and instrumental noise of the Planck satellite. These non-Gaussian simulations are obtained as perturbations of a Gaussian field in two different ways which introduce a small level of skewness or kurtosis in the distribution. A comparison with a classical estimator, the genus, is also shown. We find that the Gaussian curvature is the best of our estimators in all the considered cases. Therefore we propose the use of this quantity as a particularly useful test to look for non-Gaussianity in the CMB.
rate research
Read More
We propose a fast and efficient bispectrum statistic for Cosmic Microwave Background (CMB) temperature anisotropies to constrain the amplitude of the primordial non-Gaussian signal measured in terms of the non-linear coupling parameter f_NL. We show how the method can achieve a remarkable computational advantage by focussing on subsets of the multipole configurations, where the non-Gaussian signal is more concentrated. The detection power of the test, increases roughly linearly with the maximum multipole, as shown in the ideal case of an experiment without noise and gaps. The CPU-time scales as l_{max}^3 instead of l_{max}^5 for the full bispectrum which for Planck resolution l_{max} sim 3000 means an improvement in speed of a factor 10^7 compared to the full bispectrum analysis with minor loss in precision. We find that the introduction of a galactic cut partially destroys the optimality of the configuration, which will then need to be dealt with in the future. We find for an ideal experiment with l_{max}=2000 that upper limits of f_{NL}<8 can be obtained at 1 sigma. For the case of the WMAP experiment, we would be able to put limits of |f_{NL}|<40 if no galactic cut were present. Using the real data with galactic cut, we obtain an estimate of -80<f_{NL}<80 and -160<f_{NL}<160 at 1 and 2 sigma respectively.
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 introduce the numbers of hot and cold spots, $n_h$ and $n_c$, of excursion sets of the CMB temperature anisotropy maps as statistical observables that can discriminate different non-Gaussian models. We numerically compute them from simulations of non-Gaussian CMB temperature fluctuation maps. The first kind of non-Gaussian model we study is the local type primordial non-Gaussianity. The second kind of models have some specific form of the probability distribution function from which the temperature fluctuation value at each pixel is drawn, obtained using HEALPIX. We find the characteristic non-Gaussian deviation shapes of $n_h$ and $n_c$, which is distinct for each of the models under consideration. We further demonstrate that $n_h$ and $n_c$ carry additional information compared to the genus, which is just their linear combination, making them valuable additions to the Minkowski Functionals in constraining non-Gaussianity.
The non-Gaussianity of inflationary perturbations, as encoded in the bispectrum (or 3-point correlator), has become an important additional way of distinguishing between inflation models, going beyond the linear Gaussian perturbation quantities of the power spectrum. This habilitation thesis provides a review of my work on both the theoretical and the observational aspects of these non-Gaussianities. In the first part a formalism is described, called the long-wavelength formalism, that provides a way to compute the non-Gaussianities in multiple-field inflation. Applications of this formalism to various classes of models, as well as its extensions, are also treated. In the second part an estimator is described, called the binned bispectrum estimator, that allows the extraction of information about non-Gaussianities from data of the cosmic microwave background radiation (CMB). It was in particular one of the three estimators applied to the data of the Planck satellite to provide the currently best constraints on primordial non-Gaussianity. Various extensions of the estimator and results obtained are also discussed.
We investigate the use of wavelet transforms in detecting and characterising non-Gaussian structure in maps of the cosmic microwave background (CMB). We apply the method to simulated maps of the Kaiser-Stebbins effect due to cosmic strings onto which Gaussian signals of varying amplitudes are superposed. We find the method significantly outperforms standard techniques based on measuring the moments of the pixel temperature distribution. We also compare the results with those obtained using techniques based on Minkowski functionals, and we again find the wavelet method to be superior. In particular, using the wavelet technique, we find that it is possible to detect non-Gaussianity even in the presence of a superposed Gaussian signal with five times the rms amplitude of the original cosmic string map. We also find that the wavelet technique is useful in characterising the angular scales at which the non-Gaussian signal occurs.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
