Non-Gaussianity from inflation: theory and observations

We present limits to the amplitude of non-Gaussian primordial fluctuations in the WMAP 1 yr cosmic microwave background sky maps. A nonlinear coupling parameter, fNL, characterizes the amplitude of a quadratic term in the primordial potential. We use two statistics: one is a cubic statistic which measures phase correlations of temperature fluctuations after combining all configurations of the angular bispectrum. The other uses the Minkowski functionals to measure the morphology of the sky maps. Both methods find the WMAP data consistent with Gaussian primordial fluctuations and establish limits, -58 < fNL < 134, at 95% confidence. There is no significant frequency or scale dependence of fNL. The WMAP limit is 30 times better than COBE and validates that the power spectrum can fully characterize statistical properties of CMB anisotropy in the WMAP data to a high degree of accuracy. Our results also validate the use of a Gaussian theory for predicting the abundance of clusters in the local universe. We detect a point-source contribution to the bispectrum at 41 GHz, bsrc = (9.5 ? 4.4) ? 10-5 ?K3 sr2, which gives a power spectrum from point sources of csrc = (15 ? 6) ? 10-3 ?K2 sr in thermodynamic temperature units. This value agrees well with independent estimates of source number counts and the power spectrum at 41 GHz, indicating that bsrc directly measures residual source contributions.

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First-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Tests of Gaussianity

hypothesis. The longwave part of the microwave background spectrum is quite well described by the Rayleigh-leans law. In the shortwave part the intensity is observed to decrease in accordance with the blackb ody spectrum. The radiation is extremely isotropic on both large and small scales. There is no noticeable polarization. Interest has now shifted to departures of the spectrum from that of a blackbody. Also of great interest are measurements of angular anisotropy, small-scale angular fluctuations, and polarization. What is known already is that these distortions and deviations (both spectral and angular) are small. We believe the universe may never have been completely uniform. Even in the earliest stages there may have been small perturbations of matter and radiation densities, and ofthe velocit y field. The fireball h ypothesis requires such perturbations to account for the formation of galaxies and clusters of galaxies. Observations of the microwave background are a powerful method of investigating such pertu rbations. Even perturbations that are dissipated by viscosity, thermal conductivity, and nonlinear effects too early to influence the present structure of the universe could have dis torted

Radiation as a probe of the contemporary structure and history of the universe

A non-Gaussian detection in the Wilkinson Microwave Anisotropy Probe (WMAP) first-year data is reported. The detection has been found in the combined Q - V - W map proposed by the WMAP team after applying a wavelet technique based on the spherical Mexican hat wavelet (SMHW). The skewness and the kurtosis of the SMHW coefficients are calculated at different scales (ranging from a few arcminutes to tens of degrees). A non-Gaussian signal is detected at scales of the SMHW around 4° (size in the sky of around 10°). The right-tail probability of the detection is ≈0.4%. In addition, a study of Gaussianity is performed in each hemisphere. The northern hemisphere is compatible with Gaussianity, whereas the southern one deviates from Gaussianity with a right-tail probability of ≈0.1%. Systematics, foregrounds, and uncertainties in the estimation of the cosmological parameters are carefully studied in order to identify the possible source of non-Gaussianity. The detected deviation from Gaussianity is not found to be caused by systematic effects: (1) Each one of the Q, V, and W receivers shows the same non-Gaussianity pattern. (2) Several combinations of the different receivers at each frequency band—which highly reduce the cosmic microwave background (CMB) and the foreground emissions—do not show this non-Gaussian pattern. Similarly, Galactic foregrounds show a negligible contribution to the non-Gaussian detection: non-Gaussianity is detected in all the WMAP maps (from 23 to 94 GHz), and no frequency dependence is observed. Moreover, the expected foreground contribution to the combined WMAP map was added to CMB Gaussian simulations showing a behavior compatible with the Gaussian model. The influence of uncertainties in the CMB power spectrum estimation are also quantified. Hence, possible intrinsic temperature fluctuations (such as secondary anisotropies and primordial features) cannot be rejected as the source of this non-Gaussian detection. We remark that our result implies not only asymmetries north/south—like other previous WMAP analyses—but also a direct non-Gaussian detection.

https://iopscience.iop.org/article/10.1086/421007/pdf

Detection of Non-Gaussianity in the Wilkinson Microwave Anisotropy Probe First-Year Data Using Spherical Wavelets

Using the recently developed effective field theory of inflation, we argue that the size and the shape of the non-Gaussianities generated by single-field inflation are generically well described by two parameters: fNLequil, which characterizes the size of the signal that is peaked on equilateral configurations, and fNLorthog, which instead characterizes the size of the signal which is peaked both on equilateral configurations and flat-triangle configurations (with opposite signs). The shape of non-Gaussianities associated with fNLorthog is orthogonal to the one associated to fNLequil, and former analysis have been mostly blind to it. We perform the optimal analysis of the WMAP 5-year data for both of these parameters. We find no evidence of non-Gaussianity, and we have the following constraints: −125 ≤ fNLequil ≤ 435, −369 ≤ fNLorthog ≤ 71 at 95% CL. We show that both of these constraints can be translated into limits on parameters of the Lagrangian of single-field inflation. For one of them, the speed of sound of the inflaton fluctuations, we find that it is either bounded to be cs ≥ 0.011 at 95% CL. or alternatively to be so small that the higher-derivative kinetic term dominate at horizon crossing. We are able to put similar constraints on the other operators of the inflaton Lagrangian.

http://iopscience.iop.org/article/10.1088/1475-7516/2010/01/028/pdf

Non-Gaussianities in single field inflation and their optimal limits from the WMAP 5-year data

We propose an estimator for the trispectrum of a scalar random field on a sphere, discuss its geometrical and statistical properties, and outline its implementation. By estimating the trispectrum of the 4 yr COBE Differential Microwave Radiometer experiment data (in HEALPix pixelization), we find new evidence of a non-Gaussian signal associated with a known systematic effect. We find that by removing data from the sky maps for those periods of time perturbed by this effect, the amplitudes of the trispectrum coefficients become completely consistent with predictions for a Gaussian sky. These results reinforce the importance of statistical methods based in harmonic space for quantifying non-Gaussianity.

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The Trispectrum of the 4 Year COBE DMR Data

We investigate the potential of next-generation surveys of the cosmic microwave background and large-scale structure, to constrain the nature of dark energy, by means of the cross-correlation of the Integrated Sachs-Wolfe effect with the galaxy distribution. We first complete a signal-to-noise analysis to decide the most appropriate properties of a survey required to detect the correlated signal at a significance level of higher than 4σ. We find that more than 35% of the sky should be covered, the galaxy distribution should be probed out to a median redshift higher than 0.8, and the number of galaxies detected should be higher than a few per squared arcmin. We then consider in particular forthcoming surveys DUNE, LSST, SNAP, PanSTARRS. We independently compute the constraints that the DUNE survey can place on the nature of dark energy, by means of different parametrisations of its equation of state, using a standard Fisher matrix analysis. We confirm that, with respect to limits placed by pure CMB, cross-correlation constraints can help to break the degeneracies between dark energy and cosmological parameters. The strength of the constraints is not, of course, independent of the dark-energy model. The constraints are complementary to, despite being weaker than, some other probes of dark energy such as gravitational weak-lensing, because they are sensitive to the high-redshift behaviour of the dark energy.

/pdf/optimising-large-galaxy-surveys-for-isw-detection-2pk5n0kjjg.pdf

Optimising large galaxy surveys for ISW detection

In the context of the present and future Cosmic Microwave Background (CMB) experiments, going beyond the information provided by the power spectrum has become necessary in order to tightly constrain the cosmological model. The non-Gaussian signatures in the CMB represent a very promising tool to probe the early universe and the structure formation epoch. We present the results of a comparison between two families of non-Gaussian estimators: The first act on the wavelet space (skewness and excess kurtosis of the wavelet coefficients) and the second group on the Fourier space (bi- and trispectrum). We compare the relative sensitivities of these estimators by applying them to three different data sets meant to reproduce the majority of possible non-Gaussian contributions to the CMB. We find that the skewness in the wavelet space is slightly more sensitive than the bispectrum. For the four point estimators, we find that the excess kurtosis of the wavelet coefficients has very similar capabilities than the diagonal trispectrum while a near-diagonal trispectrum seems to be less sensitive to non-Gaussian signatures.

/pdf/non-gaussianity-comparing-wavelet-and-fourier-based-methods-6cil62iq93.pdf

Non-Gaussianity: Comparing wavelet and Fourier based methods

We present analytical expressions for the Fourier analog of the CMB three-point and four-point correlation functions, the spatial bispectrum and trispectrum, of the Ostriker and Vishniac effect in the linear and mildly nonlinear regime. Through this systematic study, we illustrate a technique to tackle the calculation of such statistics making use of the effects of its small-angle and vector-like properties through the Limber approximation. Finally we discuss its configuration dependence and detectability in the context of Gaussian theories for the currently favored flat Lambda CDM cosmology.

The Bispectrum and the Trispectrum of the Ostriker and Vishniac Effect

We review the physics of the Grishchuk-Zel'dovich effect which describes the impact of large amplitude, superhorizon gravitational field fluctuations on the cosmic microwave background anisotropy power spectrum. Using the latest determination of the spectrum by the Wilkinson Microwave Anisotropy Probe satellite, we infer a lower limit on the present length scale of such fluctuations of $3.9\ifmmode\times\else\texttimes\fi{}{10}^{3}$ times the cosmological particle horizon (at the 95% confidence level).

P. G. Castro

Papers

The Trispectrum of the 4 Year COBE DMR Data

Optimising large galaxy surveys for ISW detection

Non-Gaussianity: Comparing wavelet and Fourier based methods

The Bispectrum and the Trispectrum of the Ostriker and Vishniac Effect

Scale of homogeneity of the universe from WMAP