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Scale-dependent non-Gaussianity probes inflationary physics

Christian T. Byrnes, Mischa Gerstenlauer, Sami Nurmi, Gianmassimo Tasinato, David Wands

Abstract

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.

Scale-dependent non-Gaussianity probes inflationary physics

Abstract

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.

Paper Structure

This paper contains 16 sections, 84 equations, 2 figures.

Table of Contents

  1. Introduction
  2. General results
  3. Two point function and power spectrum
  4. Three point function and $f_{\rm NL}$
  5. Four point function, $g_{\rm NL}$ and $\tau_{\rm NL}$
  6. General single field case
  7. Two field models of inflation
  8. Limiting cases
  9. Isocurvature single field
  10. Modulated reheating
  11. Two-field local case
  12. Shape dependence
  13. Curvature perturbation in coordinate space
  14. Conclusions
  15. Explicit expressions for $n_{f,ab}$ and $n_{g,ab}$
  16. ...and 1 more sections

Figures (2)

  • Figure 1: Behavior of the quantity $\partial\,\ln{f_{\rm NL}}/ \partial \ln{\alpha}$, as a simultaneous function of $x$ (taken between $0$ and $1.5$) and of $\cos{\theta}$. The two plots represent the same figure from two different points of view, that emphasize respectively the dependence on $x$ and on $\cos{\theta}$. We have chosen $n_{f_{\rm NL}}=0.01$.
  • Figure 2: Absolute values of the functions $W$ and $I$ plotted on logarithmic scales for the choice $k_i=4$ (in arbitrary units).