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Effective field theory approach to quasi-single field inflation and effects of heavy fields

Toshifumi Noumi, Masahide Yamaguchi, Daisuke Yokoyama

TL;DR

This work develops a comprehensive effective field theory framework for quasi-single field inflation by constructing the most general action consistent with unbroken time-dependent spatial diffeomorphism and including a massive isocurvature field $\sigma$ with $m_\sigma\sim H$. By applying the St"uckelberg trick, the Goldstone boson $\pi$ is introduced and its decoupling regime analyzed, enabling tractable calculations of the power spectrum and non-Gaussianities. The authors classify action terms up to cubic order, provide explicit mappings to Chen–Wang-type models and heavy-field scenarios, and study both constant and sudden turning trajectories to illustrate how heavy fields imprint observable signatures, especially in the squeezed limit. The framework yields quantitative predictions for the power spectrum corrections and the momentum dependence of $\langle\zeta\zeta\zeta\rangle$ that interpolate between local and equilateral shapes, offering a systematic tool for exploring multi-field inflation scenarios and the role of heavy particles during inflation.

Abstract

We apply the effective field theory approach to quasi-single field inflation, which contains an additional scalar field with Hubble scale mass other than inflaton. Based on the time-dependent spatial diffeomorphism, which is not broken by the time-dependent background evolution, the most generic action of quasi-single field inflation is constructed up to third order fluctuations. Using the obtained action, the effects of the additional massive scalar field on the primordial curvature perturbations are discussed. In particular, we calculate the power spectrum and discuss the momentum-dependence of three point functions in the squeezed limit for general settings of quasi-single field inflation. Our framework can be also applied to inflation models with heavy particles. We make a qualitative discussion on the effects of heavy particles during inflation and that of sudden turning trajectory in our framework.

Effective field theory approach to quasi-single field inflation and effects of heavy fields

TL;DR

This work develops a comprehensive effective field theory framework for quasi-single field inflation by constructing the most general action consistent with unbroken time-dependent spatial diffeomorphism and including a massive isocurvature field with . By applying the St"uckelberg trick, the Goldstone boson is introduced and its decoupling regime analyzed, enabling tractable calculations of the power spectrum and non-Gaussianities. The authors classify action terms up to cubic order, provide explicit mappings to Chen–Wang-type models and heavy-field scenarios, and study both constant and sudden turning trajectories to illustrate how heavy fields imprint observable signatures, especially in the squeezed limit. The framework yields quantitative predictions for the power spectrum corrections and the momentum dependence of that interpolate between local and equilateral shapes, offering a systematic tool for exploring multi-field inflation scenarios and the role of heavy particles during inflation.

Abstract

We apply the effective field theory approach to quasi-single field inflation, which contains an additional scalar field with Hubble scale mass other than inflaton. Based on the time-dependent spatial diffeomorphism, which is not broken by the time-dependent background evolution, the most generic action of quasi-single field inflation is constructed up to third order fluctuations. Using the obtained action, the effects of the additional massive scalar field on the primordial curvature perturbations are discussed. In particular, we calculate the power spectrum and discuss the momentum-dependence of three point functions in the squeezed limit for general settings of quasi-single field inflation. Our framework can be also applied to inflation models with heavy particles. We make a qualitative discussion on the effects of heavy particles during inflation and that of sudden turning trajectory in our framework.

Paper Structure

This paper contains 29 sections, 186 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Effective field theory approach and quasi-single field inflation
  3. Effective field theory approach to inflation
  4. Quasi-single field inflation
  5. Most generic action of quasi-single field inflation
  6. Action in the unitary gauge
  7. Ambiguity of the action in the unitary gauge
  8. Normalization $1:$ $\alpha_1+\alpha_2=1$.
  9. Normalization $2:$ $\alpha_4=\beta_3=\gamma_2=0$.
  10. Normalization $3:$ $\alpha_1=1$, $\gamma_5=0$.
  11. Action for the Goldstone boson and the decoupling regime
  12. Examples
  13. Original model discussed by Chen and Wang
  14. Effects of heavy particles
  15. A class of two-field models
  16. ...and 14 more sections

Figures (4)

  • Figure 1: $\mathcal{C}_{ij}$'s for fixed $r_s=c_\sigma/c_\pi$. The dots are numerical results for $r_s=0.1$ (red), $0.3$ (orange), $1$ (yellow), $3$ (green), and $10$ (blue). The curves are analytic results for $r_s=1$ obtained in the next subsection.
  • Figure 2: $\mathcal{C}_{ij}$'s for fixed $m_\sigma$. The dots are numerical results for $m_\sigma/H=1.2$ (red), $1.6$ (yellow), $2.0$ (green), and $4.0$ (blue).
  • Figure 3: $\mathcal{F}_\nu$ for fixed $c_\pi k_\ast\Delta\tau$ and $c_\pi=c_\sigma$
  • Figure 4: Feynman diagrams for the first term of (\ref{['before_squeeze']}). The solid lines denote the propagations of $\pi$ and the dotted lines denote those of $\sigma$.