The effect of the linear term on the wavelet estimator of primordial non-Gaussianity

In this work we present constraints on different shapes of primordial non-Gaussianity using the Wilkinson Microwave Anisotropy Probe (WMAP) 7-year data and the spherical Mexican hat wavelet fnl estimator including the linear term correction. In particular we focus on the local, equilateral and orthogonal shapes. We first analyse the main statistical properties of the wavelet estimator and show the conditions to reach optimality. We include the linear term correction in our estimators and compare the estimates with the values already published using only the cubic term. The estimators are tested with realistic WMAP simulations with anisotropic noise and the WMAP KQ75 sky cut. The inclusion of the linear term correction shows a negligible improvement (< 1 per cent) in the error-bar for any of the shapes considered. The results of this analysis show that, in the particular case of the wavelet estimator, the optimality for WMAP anisotropy levels is basically achieved with the mean subtraction and in practical terms there is no need of including a linear term once the mean has been subtracted. Our best estimates are now: local fnl = 39.0 +/ 21.4, equilateral fnl = -62.8 +/- 154.0 and orthogonal fnl = -159.8 +/- 115.1 (all cases 68 per cent CL). We have also computed the expected linear term correction for simulated Planck maps with anisotropic noise at 143 GHz following the Planck Sky Model and including a mask. The improvement achieved in this case for the local fnl error-bar is also negligible (0.4 per cent).Comment: 8 pages, 5 figures, 4 tables. Minor revision, one figure added, accepted for publication in MNRA

Geometrical estimators as a test of Gaussianity in the CMB

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.Comment: 9 pages, 6 postscript figures, submitted to MNRA

Kramers equation for a charged Brownian particle: The exact solution

We report the exact fundamental solution for Kramers equation associated to a brownian gas of charged particles, under the influence of homogeneous (spatially uniform) otherwise arbitrary, external mechanical, electrical and magnetic fields. Some applications are presented, namely the hydrothermodynamical picture for Brownian motion in the long time regime.Comment: minor correction

Protectionist Responses to the Crisis: Global Trends and Implications

In this paper we take a systematic look at recent trends in global protectionism and at the potential implications of a protectionist backlash for economic growth, using results from the recent economic literature and new model simulations. We find that there has so far been a moderate increase in actual protectionist measures to restrict trade through tariff and non-tariff barriers. At the same time, evidence from surveys shows that public pressure for more economic protection has been mounting since the mid-2000s, and has possibly intensified since the start of the financial crisis. However, no World Trade Organization (WTO) member has retreated into widespread trade restrictions or protectionism to date. Our model-based simulations suggest that the impairment of the global flow of trade would hamper the recovery from the crisis, as well as the long-term growth of the global economy. At the same time, it is unlikely that protectionism would help to correct existing current account imbalances. Moreover, the countries implementing protectionist measures should expect a deterioration of their international competitiveness, which would further affect the potential for longer-term real GDP growth.Protectionism ; trade ; financial crisis ; competitiveness ; World Trade Organization ; global imbalances.

A linear filter to reconstruct the ISW effect from CMB and LSS observations

The extraction of a signal from some observational data sets that contain different contaminant emissions, often at a greater level than the signal itself, is a common problem in Astrophysics and Cosmology. The signal can be recovered, for instance, using a simple Wiener filter. However, in certain cases, additional information may also be available, such as a second observation which correlates to a certain level with the sought signal. In order to improve the quality of the reconstruction, it would be useful to include as well this additional information. Under these circumstances, we have constructed a linear filter, the linear covariance-based filter, that extracts the signal from the data but takes also into account the correlation with the second observation. To illustrate the performance of the method, we present a simple application to reconstruct the so-called Integrated Sachs-Wolfe effect from simulated observations of the Cosmic Microwave Background and of catalogues of galaxies.Comment: 8 pages, 6 figures, accepted for publication in the IEEE Journal of Selected Topics in Signal Processin

Non-Gaussianity analysis on local morphological measures of WMAP data

The decomposition of a signal on the sphere with the steerable wavelet constructed from the second Gaussian derivative gives access to the orientation, signed-intensity, and elongation of the signal's local features. In the present work, the non-Gaussianity of the WMAP temperature data of the cosmic microwave background (CMB) is analyzed in terms of the first four moments of the statistically isotropic random fields associated with these local morphological measures, at wavelet scales corresponding to angular sizes between 27.5 arcminutes and 30 degrees on the celestial sphere. While no detection is made neither in the orientation analysis nor in the elongation analysis, a strong detection is made in the excess kurtosis of the signed-intensity of the WMAP data. The non-Gaussianity is observed with a significance level below 0.5% at a wavelet scale corresponding to an angular size around 10 degrees, and confirmed at neighbour scales. This supports a previous detection of an excess of kurtosis in the wavelet coefficient of the WMAP data with the axisymmetric Mexican hat wavelet (Vielva et al. 2004). Instrumental noise and foreground emissions are not likely to be at the origin of the excess of kurtosis. Large-scale modulations of the CMB related to some unknown systematics are rejected as possible origins of the detection. The observed non-Gaussianity may therefore probably be imputed to the CMB itself, thereby questioning the basic inflationary scenario upon which the present concordance cosmological model relies. Taking the CMB temperature angular power spectrum of the concordance cosmological model at face value, further analysis also suggests that this non-Gaussianity is not confined to the directions on the celestial sphere with an anomalous signed-intensity.Comment: 10 pages, 3 figures. Version 2 includes minor changes to match version accepted for publication in MNRA

Reconstructing the Inflaton Potential

A review is presented of recent work by the authors concerning the use of large scale structure and microwave background anisotropy data to determine the potential of the inflaton field. The importance of a detection of the stochastic gravitational wave background is emphasised, and some preliminary new results of tests of the method on simulated data sets with uncertainties are described. (Proceedings of ``Unified Symmetry in the Small and in the Large'', Coral Gables, 1994)Comment: 13 pages, uuencoded postscript file with figures included (LaTeX file available from ARL), FERMILAB-Conf 94/189