CMB Constraints on Primordial non-Gaussianity from the Bispectrum (f_{NL}) and Trispectrum (g_{NL} and τ_{NL}) and a New Consistency Test of Single-Field Inflation

Abstract

We outline the expected constraints on non-Gaussianity from the cosmic microwave background (CMB) with current and future experiments, focusing on both the third (f_{NL}) and fourth-order (g_{NL} and τ_{NL}) amplitudes of the local configuration or non-Gaussianity. The experimental focus is the skewness (two-to-one) and kurtosis (two-to-two and three-to-one) power spectra from weighted maps. In adition to a measurement of τ_{NL} and g_{NL} with WMAP 5-year data, our study provides the first forecasts for future constraints on g_{NL}. We describe how these statistics can be corrected for the mask and cut-sky through a window function, bypassing the need to compute linear terms that were introduced for the previous-generation non-Gaussianity statistics, such as the skewness estimator. We discus the ratio A_{NL} = τ_{NL}/(6f_{NL}/5)^2 as an additional test of single-field inflationary models and discuss the physical significance of each statistic. Using these estimators with WMAP 5-Year V+W-band data out to l_{max}=600 we constrain the cubic order non-Gaussianity parameters τ_{NL}, and g_{NL} and find -7.4 < g_{NL}/10^5 < 8.2 and -0.6 < τ_{NL}/10^4 < 3.3 improving the previous COBE-based limit on τ_{NL} < 10^8 nearly four orders of magnitude with WMAP.

15 pages. 14 figures

References in corpus (9)

• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Non-Gaussianities in two-field inflation
• Detection of primordial non-Gaussianity (fNL) in the WMAP 3-year data at above 99.5% confidence
• Non-Gaussianity in the modulated reheating scenario
• The shape of primordial non-Gaussianity and the CMB bispectrum
• Primordial trispectrum from inflation
• Optimal limits on f_{NL}^{local} from WMAP 5-year data
• Angular Trispectrum of CMB Temperature Anisotropy from Primordial Non-Gaussianity with the Full Radiation Transfer Function
• Curvaton Dynamics and the Non-Linearity Parameters in Curvaton Model

Cited by in corpus (17)

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• Scale-dependence of Non-Gaussianity in the Curvaton Model
• Testing the Running of non-Gaussianity through the CMB mu-distortion and the Halo Bias
• Non-Gaussianity Consistency Relation for Multi-field Inflation
• Consistency Relations for the Conformal Mechanism
• Limits on Second-Order Non-Gaussianity from Minkowski Functionals of WMAP Data
• First constraints on the running of non-Gaussianity
• Transport equations for the inflationary trispectrum
• The CMB Bispectrum, Trispectrum, non-Gaussianity, and the Cramer-Rao Bound
• Examining the consistency relations describing the three-point functions involving tensors
• A Constraint On the Integrated Mass Power Spectrum out to z = 1100 from Lensing of the Cosmic Microwave Background
• The scalar bi-spectrum during preheating in single field inflationary models
• On primordial trispectrum from exchanging scalar modes in general multiple field inflationary models