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

The bispectrum of matter perturbations from cosmic strings

We present the first calculation of the bispectrum of the matter perturbations induced by cosmic strings. The calculation is performed in two different ways: the first uses the unequal time correlators (UETCs) of the string network - computed using a Gaussian model previously employed for cosmic string power spectra. The second approach uses the wake model, where string density perturbations are concentrated in sheet-like structures whose surface density grows with time. The qualitative and quantitative agreement of the two gives confidence to the results. An essential ingredient in the UETC approach is the inclusion of compensation factors in the integration with the Green's function of the matter and radiation fluids, and we show that these compensation factors must be included in the wake model also. We also present a comparison of the UETCs computed in the Gaussian model, and those computed in the unconnected segment model (USM) used by the standard cosmic string perturbation package CMBACT. We compare numerical estimates for the bispectrum of cosmic strings to those produced by perturbations from an inflationary era, and discover that, despite the intrinsically non-Gaussian nature of string-induced perturbations, the matter bispectrum is unlikely to produce competitive constraints on a population of cosmic strings

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

Constraining Galileon inflation

In this short paper, we present constraints on the Galileon inflationary model from the CMB bispectrum. We employ a principal-component analysis of the independent degrees of freedom constrained by data and apply this to the WMAP 9-year data to constrain the free parameters of the model. A simple Bayesian comparison establishes that support for the Galileon model from bispectrum data is at best weak

Constraining the WMAP9 bispectrum and trispectrum with needlets

We develop a needlet approach to estimate the amplitude of general (including non-separable) bispectra and trispectra in the cosmic microwave background, and apply this to the WMAP 9-year data. We obtain estimates for the `orthogonal' bispectrum mode, yielding results which are consistent with the WMAP 7-year data. We do not observe the frequency-dependence suggested by the WMAP team's analysis of the 9-year data. We present 1-$\sigma$ constraints on the `local' trispectrum shape \gnl/10^5= -4.1\pm 2.3, the `$c1$' equilateral model \gnl^{c_1}/10^6= -0.8\pm 2.9, and the constant model \gnl^{\rm{const}}/10^6= -0.2\pm 1.8, together with a $95\%$ confidence-level upper bound on the multifield local parameter \taunl<22000. We estimate the bias on these parameters produced by point sources. The techniques developed in this paper should prove useful for other datasets such as Planck.Comment: 21 pages - matches published versio

Preschool Children and Behaviour Problems: A Prospective Study

Toddler/child behaviour problems have received relatively little previous attention. Prior studies have implicated a wide variety of factors in the aetiology of child behaviour problems but many of these factors are correlated and little is known about their independent contributions. Four broad categories of factors have been associated with child behaviour problems: (1) maternal social and economic characteristics; (2) maternal lifestyle; (3) maternal mental state/child-rearing practices; and (4) maternal and child physical health. The study took a sample of 5296 families from the Mater-University of Queensland Study of Pregnancy (MUSP) for whom 5-year prospective data are available. The major predictors of toddler behaviour problems were the mother's and child's health, and the mother's mental state. The mother's sociostructural characteristics and lifestyle made little or no additional contribution to the prediction models. It is, however, salutary to note that the majority of children who are classified as having high levels of troublesome behaviour do not fall into any of the risk categories. A variety of explanations and interpretations of the data is considered

Non-Gaussianity in the Cosmic Microwave Background Anisotropies at Recombination in the Squeezed limit

We estimate analytically the second-order cosmic microwave background temperature anisotropies at the recombination epoch in the squeezed limit and we deduce the contamination to the primordial local non-Gaussianity. We find that the level of contamination corresponds to f_NL^{con}=O(1) which is below the sensitivity of present experiments and smaller than the value O(5) recently claimed in the literature.Comment: LaTeX file; 15 pages. Slightly revised version. Main result unchange

Influence of large local and non-local bispectra on primordial black hole abundance

Primordial black holes represent a unique probe to constrain the early universe on small scales - providing the only constraints on the primordial power spectrum on the majority of scales. However, these constraints are strongly dependent on even small amounts of non-Gaussianity, which is unconstrained on scales significantly smaller than those visible in the CMB. This paper goes beyond previous considerations to consider the effects of a bispectrum of the equilateral, orthogonal and local shapes with arbitrary magnitude upon the abundance of primordial black holes. Non-Gaussian density maps of the early universe are generated from a given bispectrum and used to place constraints on the small scale power spectrum. When small, we show that the skewness provides an accurate estimate for how the constraint depends on non-Gaussianity, independently of the shape of the bispectrum. We show that the orthogonal template of non-Gaussianity has an order of magnitude weaker effect on the constraints than the local and equilateral templates.Comment: 11 pages, 4 figures, updated to match published version in JCAP02(2016)029, Journal of Cosmology and Astroparticle Physics, Volume 2016, February 201

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