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Trispectrum from Ghost Inflation

Keisuke Izumi, Shinji Mukohyama

TL;DR

This work computes the trispectrum of primordial curvature perturbations in ghost inflation, revealing two leading contributions: a contact-term from the quartic interaction and a scalar-exchange term from two cubic interactions. Each contribution yields a distinct $\tau_{NL}$-type statistic, with equilateral configurations peaking and signs depending on the couplings. The combined results show $\tau_{NL}$ typically of order $10^4$, offering a promising avenue for Planck- or future-era constraints to distinguish ghost inflation from DBI and other models via the trispectrum’s shape and amplitude. The analysis highlights both similarities and key differences in angular dependence relative to DBI inflation, suggesting trispectrum templates as a diagnostic for early-Universe physics.

Abstract

Ghost inflation predicts almost scale-invariant primordial cosmological perturbations with relatively large non-Gaussianity. The bispectrum is known to have a large contribution at the wavenumbers forming an equilateral triangle and the corresponding nonlinear parameter $f_{NL}^{equil}$ is typically of order $O(10^2)$. In this paper we calculate trispectrum from ghost inflation and show that the corresponding nonlinear parameter $τ_{NL}$ is typically of order $O(10^4)$. We investigate the shape dependence of the trispectrum and see that it has some features different from DBI inflation. Therefore, our result may be useful as a template to distinguish ghost inflation from other models of inflation by future experiments.

Trispectrum from Ghost Inflation

TL;DR

This work computes the trispectrum of primordial curvature perturbations in ghost inflation, revealing two leading contributions: a contact-term from the quartic interaction and a scalar-exchange term from two cubic interactions. Each contribution yields a distinct -type statistic, with equilateral configurations peaking and signs depending on the couplings. The combined results show typically of order , offering a promising avenue for Planck- or future-era constraints to distinguish ghost inflation from DBI and other models via the trispectrum’s shape and amplitude. The analysis highlights both similarities and key differences in angular dependence relative to DBI inflation, suggesting trispectrum templates as a diagnostic for early-Universe physics.

Abstract

Ghost inflation predicts almost scale-invariant primordial cosmological perturbations with relatively large non-Gaussianity. The bispectrum is known to have a large contribution at the wavenumbers forming an equilateral triangle and the corresponding nonlinear parameter is typically of order . In this paper we calculate trispectrum from ghost inflation and show that the corresponding nonlinear parameter is typically of order . We investigate the shape dependence of the trispectrum and see that it has some features different from DBI inflation. Therefore, our result may be useful as a template to distinguish ghost inflation from other models of inflation by future experiments.

Paper Structure

This paper contains 14 sections, 117 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Review of ghost inflation
  3. The Model
  4. Powerspectrum
  5. Bispectrum
  6. Trispectrum
  7. contact term contribution
  8. scalar exchange contribution
  9. Summary and Discussion
  10. Review of in-in formalism
  11. Interaction term of Hamiltonian
  12. Detailed calculations
  13. contact term contribution
  14. scalar exchange contribution

Figures (10)

  • Figure 1: The diagram for the contact term contribution.
  • Figure 2: The diagram for the scalar exchange contribution.
  • Figure 3: This plot shows the dependence of $T_{\zeta , cc}(k,C_2,C_3,C_4)$ on $C_2$ and $C_3$, where $C_4=-1-C_2-C_3$. The horizontal axis is rescaled by the value at $C_2=C_3=-1/3$.
  • Figure 4: This plot shows the dependence of $\tau_{NL}^{cc}(k,C_2,C_3,C_4)$ on $C_2$ and $C_3$, where $C_4=-1-C_2-C_3$. The horizontal axis is rescaled by the value at $C_2=C_3=-1/3$.
  • Figure 5: This is the plot of the function $A(C)$.
  • ...and 5 more figures