Non-Gaussian Mode Coupling and the Statistical Cosmological Principle

Abstract

Local-type primordial non-Gaussianity couples statistics of the curvature perturbation ζon vastly different physical scales. Because of this coupling, statistics (i.e. the polyspectra) of ζin our Hubble volume may not be representative of those in the larger universe -- that is, they may be biased. The bias depends on the local background value of ζ, which includes contributions from all modes with wavelength k ~< H_0 and is therefore enhanced if the entire post-inflationary patch is large compared with our Hubble volume. We study the bias to locally-measured statistics for general local-type non-Gaussianity. We consider three examples in detail: (i) the usual fNL, gNL model, (ii) a strongly non-Gaussian model with ζ~ ζ_G^p, and (iii) two-field non-Gaussian initial conditions. In each scenario one may generate statistics in a Hubble-size patch that are weakly Gaussian and consistent with observations despite the fact that the statistics in the larger, post-inflationary patch look very different.

34 pages, 8 Figures. references added, typos corrected; v3 matches JCAP version

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• Constraints on Gauge Field Production during Inflation
• The next non-Gaussianity frontier: what can a measurement with $\sigma (f_{\mathrm{NL}})\lesssim 1$ tell us about multifield inflation?
• Cosmic variance in inflation with two light scalars
• Scale-dependent non-Gaussianity and the CMB Power Asymmetry
• Correlating CMB Spectral Distortions with Temperature: what do we learn on Inflation?
• Generating the cosmic microwave background power asymmetry with $g_{NL}$
• Statistics of Anisotropies in Inflation with Spectator Vector Fields
• Cosmic Variance of the Spectral Index from Mode Coupling
• Influence of Reheating on the Trispectrum and its Scale Dependence
• Super cosmic variance from mode-coupling: A worked example
• Non-local bispectra from super cosmic variance
• Local Observables in a Landscape of Infrared Gauge Modes
• Constraining primordial and gravitational mode coupling with the position-dependent bispectrum of the large-scale structure
• Single-Field Inflation and the Local Ansatz: Distinguishability and Consistency
• Statistical anisotropies in temperature and polarization fluctuations from a scale-dependent trispectrum
• Higher moments of primordial non-Gaussianity and N-body simulations
• Influence of Unobservable Modes on Correlation Functions during Inflation
• On the space of non-Gaussian fields with single-clock bispectra