The shape of non-Gaussianities

By D. Babich, P. Creminelli, M. Zaldarriaga. 2004

564 citations recorded by the source corpus.

We study the dependence on the configuration in momentum space of the primordial three-point function of density perturbations in several different scenarios: standard slow-roll inflation, curvaton and variable decay models, ghost inflation, models with higher derivative operators and the DBI model of inflation. We define a cosine between the distributions using a measure based on the ability of experiments to distinguish between them. We find that models fall into two broad categories with fairly orthogonal distributions: models where non-Gaussianity is created on crossing the horizon during inflation and models in which the evolution beyond the horizon dominates. In the first case the three-point function is largest for equilateral triangles, while in the second the dominant contribution to the signal comes from the influence of long wavelength modes on small wavelength ones. We show that, because the distributions in these two cases are so different, translating constraints on parameters of one model to those of the other on the basis of the normalization of the three-point function for equilateral triangles can be very misleading.

Subfields: Astronomy and Astrophysics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ff9495a01547cb224c8aae668dd4def435897db6

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Citations in the corpus

Cosmology and Fundamental Physics with the Euclid Satellite (2012, background): “In order to study the observational signatures of these models we need to go beyond the local case and study the shape of non-Gaussianity [95].”
Observable non-gaussianity from gauge field production in slow roll inflation, and a challenging connection with magnetogenesis (2012, background): “Indeed, the “cosine” between our bispectrum and the local shape, as defined in [64] (this is a measure on how well a template reproduced a given bi-spectrum), is about 0.”
A review of axion inflation in the era of Planck (2013, methodology): “The shape of the bispectrum is close to the equilateral one [62]: the cosine (as defined in [63]) between the bispectrum from this mechanism and the equilateral template is 0.”
SEVEN-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP) OBSERVATIONS: COSMOLOGICAL INTERPRETATION (2010, background): “…bispectrum can arise from the curvature perturbation in the form of Φ = ΦL + f local NL Φ 2 L, where both sides are evaluated at the same location in space (ΦL is a linear Gaussian fluctuation).34 Equation (60) peaks at the socalled “squeezed” triangle for which k3 ≪ k2 ≈ k1 (Babich et al. 2004).”
Inflation and String Theory (2014, background): “—The two equilateral bispectra are not identical, so one can find a linear combination of the two operators π̇(∂iπ) 2 and π̇(3) that is orthogonal in a well-defined sense [123] to the shape (1.”
The (not so) squeezed limit of the primordial 3-point function (2011, background): “n from unity of the speed of sound [21]. It is well known that, neglecting slow-roll corrections, higher-derivative terms only give equilateral shapes, i.e. suppressed by 8 k2 L in the squeezed limit [22]. The absence of linear terms should be valid also including slow-roll corrections, though the e”
Review of local non-Gaussianity from multi-field inflation (2010, methodology): “There are several different fNL’s used in the literature which parameterise different shape dependences of the bispectrum [41, 42], the most popular being the local model discussed in this paper and the so-called equilateral model which can arise from models of inflation with noncanonical kinetic te”
Resonant non-gaussianity (2010, background): “In light of this difficulty, the authors of [14] have proposed to use a 18”
Gauge Field Production in Axion Inflation: Consequences for Monodromy, non-Gaussianity in the CMB, and Gravitational Waves at Interferometers (2011, background): “The cosine (defined in [58]) between the precise shape and the equilateral template evaluates to 0.”
Equilateral Non-Gaussianity and New Physics on the Horizon (2011, methodology): “and a shape function [29] S(x1, x2) ≡ (x1x2)(2) · Bζ(x1, x2, 1) Bζ(1, 1, 1) .”
The bispectrum of galaxies from high-redshift galaxy surveys: Primordial non-Gaussianity and non-linear galaxy bias (2007, methodology): “(5) Babich et al. (2004) and Creminelli et al. (2007) have shown that this form provides a good approximation to the bispectra predicted by higher derivatives and DBI inflationary models (Creminelli 2003; Alishahiha et al. 2004).”
Primordial non-Gaussianity from the large-scale structure (2010, background): “Although the configuration shape of the primordial bispectrum can be extremely complex in some models, there are broadly three classes of shape characterizing the local, equilateral and folded type of primordial non-Gaussianity [24, 25].”
The Effective Field Theory of Inflation (2007, background): “” refers to the momentum dependence of the 3-point function, which in these models is of the so called equilateral form [22].”
Algorithms for bispectra: Forecasting, optimal analysis, and simulation (2006, background): “Moreover, the structure of the three-point function contains precious information about the inflationary dynamics (Babich et al. 2004).”