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Spectroscopy of Masses and Couplings during Inflation

Razieh Emami

TL;DR

This work extends Quasi Single Field inflation to a multi-field iso-curvaton setup with two fields σ1, σ2 of order the Hubble scale, kinetically coupled to the inflaton and interacting among themselves. Using a turning trajectory and in-in formalism, the authors show that the power spectrum remains nearly unchanged while the bispectrum amplitude is enhanced by the iso-curvaton self-interactions, without introducing new squeezed-limit shapes. In the squeezed limit, the bispectrum shape is dominated by the lightest isocurvaton, with ν_i = sqrt{9/4 − m̂_i^2/H^2} governing the scaling, and two-shape signatures only arise when the masses are degenerate; hierarchical masses suppress heavier-field contributions. These results imply that squeezed-limit measurements can function as a particle detector for isocurvaton masses near H, while current Planck and LSS bounds constrain the interaction strength and turning velocity.

Abstract

In this work, we extend the idea of Quasi Single Field inflation to the case of multiple isocurvaton fields with masses of order of Hubble, which are coupled kinetically to the inflaton field and have some interactions among themselves. We consider the effects of these massive modes in both the size and the shape of the bispectrum. We show that the shape of the bispectrum in the squeezed limit is dominated by the lightest field and is the same as in Quasi Single Field inflation. This is a generic feature of multiple isocurvaton fields and is independent of the details of the interactions among the massive fields. When the isocurvaton fields have similar masses, we can potentially distinguish two different shapes in the squeezed limit so that the shape of the bispectrum can act as a particle detector. However, in the presence of hierarchy among the massive fields, the dominant effect is due to the lightest field.

Spectroscopy of Masses and Couplings during Inflation

TL;DR

This work extends Quasi Single Field inflation to a multi-field iso-curvaton setup with two fields σ1, σ2 of order the Hubble scale, kinetically coupled to the inflaton and interacting among themselves. Using a turning trajectory and in-in formalism, the authors show that the power spectrum remains nearly unchanged while the bispectrum amplitude is enhanced by the iso-curvaton self-interactions, without introducing new squeezed-limit shapes. In the squeezed limit, the bispectrum shape is dominated by the lightest isocurvaton, with ν_i = sqrt{9/4 − m̂_i^2/H^2} governing the scaling, and two-shape signatures only arise when the masses are degenerate; hierarchical masses suppress heavier-field contributions. These results imply that squeezed-limit measurements can function as a particle detector for isocurvaton masses near H, while current Planck and LSS bounds constrain the interaction strength and turning velocity.

Abstract

In this work, we extend the idea of Quasi Single Field inflation to the case of multiple isocurvaton fields with masses of order of Hubble, which are coupled kinetically to the inflaton field and have some interactions among themselves. We consider the effects of these massive modes in both the size and the shape of the bispectrum. We show that the shape of the bispectrum in the squeezed limit is dominated by the lightest field and is the same as in Quasi Single Field inflation. This is a generic feature of multiple isocurvaton fields and is independent of the details of the interactions among the massive fields. When the isocurvaton fields have similar masses, we can potentially distinguish two different shapes in the squeezed limit so that the shape of the bispectrum can act as a particle detector. However, in the presence of hierarchy among the massive fields, the dominant effect is due to the lightest field.

Paper Structure

This paper contains 12 sections, 157 equations, 5 figures.

Table of Contents

  1. Introduction
  2. The Setup
  3. Power Spectrum
  4. Bispectrum
  5. Squeezed limit of bispectrum
  6. Summary and Discussions
  7. The full Lagrangian up to third order
  8. Details of integrals in various forms
  9. All terms in the factorized form
  10. All of terms in the commutator form
  11. Different terms in the squeezed limit
  12. Squeezed limit amplitudes

Figures (5)

  • Figure 1: Feynman diagrams for the correction in the power spectrum. (a) is the correction due to $\sigma_{1}$ , (b) is the correction of $\sigma_{2}$ and (c) describes the sub-leading correction due to the exchange vertex between $\sigma_{1}$ and $\sigma_{2}$.
  • Figure 2: The behavior of $D(v_{i})$ in terms of $\nu_{i}$, as given in Eq. (\ref{['neumerical-power spectrum']}).
  • Figure 3: Leading corrections in the bispectrum. (a) is due to $H^{3I}_{1}$, (b) is from $H^{3I}_{2}$, (c) comes from $H^{3I}_{3}$ and (d) is from $H^{3I}_{4}$.
  • Figure 4: The plot of $(3/2 + \nu_{2} -2\nu_{1})$ for $\nu_{2}<\nu_{1}$.
  • Figure 5: $68\%$, $95\%$, and $99.7\%$ confidence intervals for $\nu$ and $f_\mathrm{NL}^{\rm QSI}$ in original quasi-single field model borrowed from PLANCK Ade:2013ydc. There is not any preferred value for $\nu$ with all values allowed at $3\sigma$.