Limits on non-Gaussianities from WMAP data

By P. Creminelli, Alberto Nicolis, L. Senatore, Max Tegmark, M. Zaldarriaga. 2005

345 citations recorded by the source corpus.

We develop a method for constraining the level of non-Gaussianity of density perturbations when the three-point function is of the ‘equilateral’ type. Departures from Gaussianity of this form are produced by single field models such as ghost or Dirac–Born–Infeld inflation and in general by the presence of higher order derivative operators in the effective Lagrangian of the inflaton. We show that the induced shape of the three-point function can be very well approximated by a factorizable form, making the analysis practical. We also show that, unless one has a full sky map with uniform noise, in order to saturate the Cramer–Rao bound for the error on the amplitude of the three-point function, the estimator must contain a piece that is linear in the data. We apply our technique to the WMAP data obtaining a constraint on the amplitude fNLequil of ‘equilateral’ non-Gaussianity: −366 < fNLequil < 238 at 95% C.L. We also apply our technique to constrain the so-called ‘local’ shape, which is predicted for example by the curvaton and variable decay width models. We show that the inclusion of the linear piece in the estimator improves the constraint over those obtained by the WMAP team, to −27 < fNLlocal < 121 at 95% C.L.

Subfields: Astronomy and Astrophysics, Oceanography

View Paper: https://www.semanticscholar.org/paper/e690589f88c8d4dfeb7ff525465741ef6bae36d2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

In Oceanography

Citations in the corpus

Primordial non-Gaussianity from the large-scale structure (2010, methodology): “Equilateral type of non-Gaussianity, which arises in inflationary models with higher derivative operators such as the DBI model, is well described by the factorizable form [27]”
Primordial Non-Gaussianities from Inflation Models (2010, methodology): “A factorizable shape ansatz for the equilateral shape that is often used in data analyses is the following [81]:”
Algorithms for bispectra: Forecasting, optimal analysis, and simulation (2006, methodology): “This generalizes the estimator proposed by Komatsu, Spergel and Wandelt (Komatsu et al. 2005) to arbitrary factorizable bispectra, and also improves it in the case of inhomogenous noise, by including the linear term in the estimator proposed in Creminelli et al. (2006).”
Effects of scale-dependent non-Gaussianity on cosmological structures (2007, methodology): “Contents”
Signatures of Initial State Modifications on Bispectrum Statistics (2009, neutral): “40 44 v2 [ he p- th ] Contents”
Non-Gaussianities in single field inflation and their optimal limits from the WMAP 5-year data (2009, background): “Each of those two operators gives rise to shapes for the nonGaussianities that are peaked on equilateral configurations but are still quite different.”
Testing Inflation with Large Scale Structure: Connecting Hopes with Reality (2014, background): “8, the equilateral template [6], f eq NL = −42± 75, and the ortogonal template [7], f NL = −25 ± 39 .”
FIVE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE OBSERVATIONS: COSMOLOGICAL INTERPRETATION (2008, positive): “In this paper we shall use the estimator that further improves upon Creminelli et al. (2006) by correcting an inadvertent numerical error of a factor of 2 in their derivation (Yadav et al. 2008).”
On the statistics of biased tracers in the Effective Field Theory of Large Scale Structures (2015, background): “For example, in the local case, f loc NL, α = 0, for the equilateral, f equil NL [43], and orthogonal, f NL [44], cases, α = 2, 7 quasi-single field inflation [45, 46], gives 0 ≤ α ≤ 3/2.”
Planck 2015 results. XVII. Constraints on primordial non-Gaussianity (2015, neutral): “This part corrects for mean-field contributions to the error bars, introduced by rotational invariance-breaking features, such as a mask or anisotropic/correlated instrumental noise (Creminelli et al. 2006; Yadav et al. 2008).”
Schwinger-Keldysh diagrammatics for primordial perturbations (2017, methodology): “We also plotted the factorizable ansatz of the equilateral shape [37] (orange).”