The CMB Bispectrum

We use a separable mode expansion estimator with WMAP data to estimate the bispectrum for all the primary families of non-Gaussian models. We review the late-time mode expansion estimator methodology which can be applied to any non-separable primordial and CMB bispectrum model, and we demonstrate how the method can be used to reconstruct the CMB bispectrum from an observational map. We extend the previous validation of the general estimator using local map simulations. We apply the estimator to the coadded WMAP 5-year data, reconstructing the WMAP bispectrum using $l<500$ multipoles and $n=31$ orthonormal 3D eigenmodes. We constrain all popular nearly scale-invariant models, ensuring that the theoretical bispectrum is well-described by a convergent mode expansion. Constraints from the local model \fnl=54.4\pm 29.4 and the equilateral model \fnl=143.5\pm 151.2 (\Fnl = 25.1\pm 26.4) are consistent with previously published results. (Here, we use a nonlinearity parameter \Fnl normalised to the local case, to allow more direct comparison between different models.) Notable new constraints from our method include those for the constant model \Fnl = 35.1 \pm 27.4 , the flattened model \Fnl = 35.4\pm 29.2, and warm inflation \Fnl = 10.3\pm 27.2. We investigate feature models surveying a wide parameter range in both the scale and phase, and we find no significant evidence of non-Gaussianity in the models surveyed. We propose a measure \barFnl for the total integrated bispectrum and find that the measured value is consistent with the null hypothesis that CMB anisotropies obey Gaussian statistics. We argue that this general bispectrum survey with the WMAP data represents the best evidence for Gaussianity to date and we discuss future prospects, notably from the Planck satellite

Optimal bispectrum constraints on single-field models of inflation

We use WMAP 9-year bispectrum data to constrain the free parameters of an 'effective field theory' describing fluctuations in single-field inflation. The Lagrangian of the theory contains a finite number of operators associated with unknown mass scales. Each operator produces a fixed bispectrum shape, which we decompose into partial waves in order to construct a likelihood function. Based on this likelihood we are able to constrain four linearly independent combinations of the mass scales. As an example of our framework we specialize our results to the case of 'Dirac-Born-Infeld' and 'ghost' inflation and obtain the posterior probability for each model, which in Bayesian schemes is a useful tool for model comparison. Our results suggest that DBI-like models with two or more free parameters are disfavoured by the data by comparison with single parameter models in the same class

The characteristics of sexual abuse in sport: A multidimensional scaling analysis of events described in media reports

Most research on sexual abuse has been conducted within family settings (Fergusson & Mullen, 1999). In recent years, following several high profile convictions and scandals, research into sexual abuse has also encompassed institutional and community settings such as sport and the church (Gallagher, 2000; Wolfe et al., 2003). Research into sexual abuse in sport, for example, began with both prevalence studies (Kirby & Greaves, 1996; Leahy, Pretty & Tenenbaum, 2002) and qualitative analyses of the processes and experiences of athlete sexual abuse (Brackenridge, 1997; Cense & Brackenridge, 2001, Toftegaard Nielsen, 2001). From such work, descriptions of the modus operandi of abusers in sport, and the experiences and consequences for athlete victims, have been provided, informing both abuse prevention work and coach education. To date, however, no study has provided empirical support for multiple associations or identified patterns of sex offending in sport in ways that might allow comparisons with research-generated models of offending outside sport. This paper reports on an analysis of 159 cases of criminally defined sexual abuse, reported in the print media over a period of 15 years. The main aim of the study was to identify the nature of sex offending in sport focusing on the methods and locations of offences. The data were analysed using multidimensional scaling (MDS), as a data reduction method, in order to identify the underlying themes within the abuse and explore the inter-relationships of behaviour, victim and context variables. The findings indicate that there are specific themes that can be identified within the perpetrator strategies that include ‘intimate’, ‘aggressive’, and ‘’dominant’ modes of interaction. The same patterns that are described here within the specific context of sport are consistent with themes that emerge from similar behavioural analyses of rapists (Canter & Heritage, 1990; Bishopp, 2003) and child molester groups (Canter, Hughes & Kirby, 1998). These patterns show a correspondence to a broader behavioural model – the interpersonal circumplex (e.g., Leary 1957). Implications for accreditation and continuing professional education of sport psychologists are noted

Non-Gaussianities in N-flation

We compute non-Gaussianities in N-flation, a string motivated model of assisted inflation with quadratic, separable potentials and masses given by the Marcenko-Pastur distribution. After estimating parameters characterizing the bi- and trispectrum in the horizon crossing approximation, we focus on the non-linearity parameter $f_{NL}$, a measure of the bispectrum; we compute its magnitude for narrow and broad spreads of masses, including the evolution of modes after horizon crossing. We identify additional contributions due to said evolution and show that they are suppressed as long as the fields are evolving slowly. This renders $\mathcal{N}$-flation indistinguishable from simple single-field models in this regime. Larger non-Gaussianities are expected to arise for fields that start to evolve faster, and we suggest an analytic technique to estimate their contribution. However, such fast roll during inflation is not expected in N-flation, leaving (p)re-heating as the main additional candidate for generating non-Gaussianities.Comment: 27 pages, 4 figures, extended references to match version accepted in JCA

Effects and Detectability of Quasi-Single Field Inflation in the Large-Scale Structure and Cosmic Microwave Background

Quasi-single field inflation predicts a peculiar momentum dependence in the squeezed limit of the primordial bispectrum which smoothly interpolates between the local and equilateral models. This dependence is directly related to the mass of the isocurvatons in the theory which is determined by the supersymmetry. Therefore, in the event of detection of a non-zero primordial bispectrum, additional constraints on the parameter controlling the momentum-dependence in the squeezed limit becomes an important question. We explore the effects of these non-Gaussian initial conditions on large-scale structure and the cosmic microwave background, with particular attention to the galaxy power spectrum at large scales and scale-dependence corrections to galaxy bias. We determine the simultaneous constraints on the two parameters describing the QSF bispectrum that we can expect from upcoming large-scale structure and cosmic microwave background observations. We find that for relatively large values of the non-Gaussian amplitude parameters, but still well within current uncertainties, galaxy power spectrum measurements will be able to distinguish the QSF scenario from the predictions of the local model. A CMB likelihood analysis, as well as Fisher matrix analysis, shows that there is also a range of parameter values for which Planck data may be able distinguish between QSF models and the related local and equilateral shapes. Given the different observational weightings of the CMB and LSS results, degeneracies can be significantly reduced in a joint analysis.Comment: 27 pages, 14 figure

Scale-dependent non-Gaussianity probes inflationary physics

We calculate the scale dependence of the bispectrum and trispectrum in (quasi) local models of non-Gaussian primordial density perturbations, and characterize this scale dependence in terms of new observable parameters. They can help to discriminate between models of inflation, since they are sensitive to properties of the inflationary physics that are not probed by the standard observables. We find consistency relations between these parameters in certain classes of models. We apply our results to a scenario of modulated reheating, showing that the scale dependence of non-Gaussianity can be significant. We also discuss the scale dependence of the bispectrum and trispectrum, in cases where one varies the shape as well as the overall scale of the figure under consideration. We conclude providing a formulation of the curvature perturbation in real space, which generalises the standard local form by dropping the assumption that f_NL and g_NL are constants.Comment: 27 pages, 2 figures. v2: Minor changes to match the published versio

Large slow-roll corrections to the bispectrum of noncanonical inflation

Nongaussian statistics are a powerful discriminant between inflationary models, particularly those with noncanonical kinetic terms. Focusing on theories where the Lagrangian is an arbitrary Lorentz-invariant function of a scalar field and its first derivatives, we review and extend the calculation of the observable three-point function. We compute the "next-order" slow-roll corrections to the bispectrum in closed form, and obtain quantitative estimates of their magnitude in DBI and power-law k-inflation. In the DBI case our results enable us to estimate corrections from the shape of the potential and the warp factor: these can be of order several tens of percent. We track the possible sources of large logarithms which can spoil ordinary perturbation theory, and use them to obtain a general formula for the scale dependence of the bispectrum. Our result satisfies the next-order version of Maldacena's consistency condition and an equivalent consistency condition for the scale dependence. We identify a new bispectrum shape available at next-order, which is similar to a shape encountered in Galileon models. If fNL is sufficiently large this shape may be independently detectable.Comment: v1: 37 pages, plus tables, figures and appendices. v2: supersedes version published in JCAP; some clarifications and more detailed comparison with earlier literature. All results unchanged. v3:improvements to some plots; text unchange

Inhomogeneous non-Gaussianity

We propose a method to probe higher-order correlators of the primordial density field through the inhomogeneity of local non-Gaussian parameters, such as f_NL, measured within smaller patches of the sky. Correlators between n-point functions measured in one patch of the sky and k-point functions measured in another patch depend upon the (n+k)-point functions over the entire sky. The inhomogeneity of non-Gaussian parameters may be a feasible way to detect or constrain higher-order correlators in local models of non-Gaussianity, as well as to distinguish between single and multiple-source scenarios for generating the primordial density perturbation, and more generally to probe the details of inflationary physics.Comment: 16 pages, 2 figures; v2: Minor changes and references added. Matches the published versio