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Large non-Gaussianities in the Effective Field Theory Approach to Single-Field Inflation: the Bispectrum

Nicola Bartolo, Matteo Fasiello, Sabino Matarrese, Antonio Riotto

TL;DR

This paper develops a comprehensive effective field theory framework for single-field inflation to third order, incorporating both standard and curvature-generated operators. By solving the scalar perturbation dynamics and performing in-in calculations, it identifies regimes where large primordial non-Gaussianity arises and characterizes the amplitudes via multiple mass scales, including $M_2$, $M_3$, and the curvature coefficients $\bar{M}_i$. A key finding is that curvature-generated interactions can produce large non-Gaussianities with flat bispectrum shapes, in addition to the familiar equilateral shapes from DBI-like terms, and this flatness is robust across wavefunction choices. The results broaden the landscape of single-field inflationary predictions and motivate trispectrum analyses to further constrain the underlying EFT parameter space and model classes.

Abstract

The methods of effective field theory are used to study generic theories of inflation with a single inflaton field and to perform a general analysis of the associated non-Gaussianities. We investigate the amplitudes and shapes of the various generic three-point correlators, the bispectra, which may be generated by different classes of single-field inflationary models. Besides the well-known results for the DBI-like models and the ghost inflationary theories, we point out that curvature-related interactions may give rise to large non-Gaussianities in the form of bispectra characterized by a flat shape which, quite interestingly, is independently produced by several interaction terms. In a subsequent work, we will perform a similar general analysis for the non-Gaussianities generated by the generic four-point correlator, the trispectrum.

Large non-Gaussianities in the Effective Field Theory Approach to Single-Field Inflation: the Bispectrum

TL;DR

This paper develops a comprehensive effective field theory framework for single-field inflation to third order, incorporating both standard and curvature-generated operators. By solving the scalar perturbation dynamics and performing in-in calculations, it identifies regimes where large primordial non-Gaussianity arises and characterizes the amplitudes via multiple mass scales, including , , and the curvature coefficients . A key finding is that curvature-generated interactions can produce large non-Gaussianities with flat bispectrum shapes, in addition to the familiar equilateral shapes from DBI-like terms, and this flatness is robust across wavefunction choices. The results broaden the landscape of single-field inflationary predictions and motivate trispectrum analyses to further constrain the underlying EFT parameter space and model classes.

Abstract

The methods of effective field theory are used to study generic theories of inflation with a single inflaton field and to perform a general analysis of the associated non-Gaussianities. We investigate the amplitudes and shapes of the various generic three-point correlators, the bispectra, which may be generated by different classes of single-field inflationary models. Besides the well-known results for the DBI-like models and the ghost inflationary theories, we point out that curvature-related interactions may give rise to large non-Gaussianities in the form of bispectra characterized by a flat shape which, quite interestingly, is independently produced by several interaction terms. In a subsequent work, we will perform a similar general analysis for the non-Gaussianities generated by the generic four-point correlator, the trispectrum.

Paper Structure

This paper contains 12 sections, 38 equations, 20 figures.

Table of Contents

  1. Introduction
  2. The inflationary action up to third order in the effective theory approach
  3. Solution to the equation of motion for the scalar degree of freedom
  4. Amplitude of the primordial non-Gaussianity
  5. Amplitudes from DBI-like interactions and first two curvature-generated terms
  6. Amplitudes from curvature-generated novel interaction terms
  7. Some general considerations on the amplitudes of non-Gaussianities
  8. The shapes of non-Gaussianities
  9. Shapes from DBI-like interactions and first two curvature-generated terms.
  10. Shapes from curvature-generated novel interaction terms.
  11. Some general considerations on the shapes of non-Gaussianities
  12. Conclusions

Figures (20)

  • Figure 1: DBI configuration on the left, obtained using exact methods; the approximated ghost shape on the right.
  • Figure 2: $A$ configuration on the left, $B$ configuration on the right.
  • Figure 3: exact DBI configuration on the left; approximated ghost shape on the right.
  • Figure 4: $A$ on the left, $B$ configuration on the right for the $M_3$-driven interaction term.
  • Figure 5: exact DBI configuration on the left; approximated ghost shape on the right.
  • ...and 15 more figures