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Inflation with multiple sound speeds: a model of multiple DBI type actions and non-Gaussianities

Yi-Fu Cai, Hai-Ying Xia

TL;DR

This work extends inflationary theory to multi-speed scenarios by modeling two DBI-type scalar sectors with independent sound speeds. It develops a generalized adiabatic/isocurvature decomposition suitable for multiple $c_s$ and analyzes linear perturbations using the ADM formalism, showing that perturbations freeze at the maximum sound horizon $c_s^{\max}/H$. In the two-DBI model, the background and perturbation spectra are computed, revealing nearly scale-invariant curvature and entropy perturbations with tilts $n_{\mathcal{R}}-1 \approx -4/{\cal N}$ and $n_{\mathcal{S}}-1 \approx -8\epsilon$, while entropy can be enhanced if one mass is light. Non-Gaussianities exhibit a dominant equilateral component governed by the smallest $c_s$, and a potentially large local component when entropy perturbations convert to curvature during late inflation, especially in cascade-like evolution. These results situate multi-speed inflation as a viable extension of N-flation and curvaton-type scenarios, with distinctive observational signatures in non-Gaussianity patterns.

Abstract

In this letter we study adiabatic and isocurvature perturbations in the frame of inflation with multiple sound speeds involved. We suggest this scenario can be realized by a number of generalized scalar fields with arbitrary kinetic forms. These scalars have their own sound speeds respectively, so the propagations of field fluctuations are individual. Specifically, we study a model constructed by two DBI type actions. We find that the critical length scale for the freezing of perturbations corresponds to the maximum sound horizon. Moreover, if the mass term of one field is much lighter than that of the other, the entropy perturbation could be quite large and so may give rise to a growth outside sound horizon. At cubic order, we find that the non-Gaussianity of local type is possibly large when entropy perturbations are able to convert into curvature perturbations. We also calculate the non-Gaussianity of equilateral type approximately.

Inflation with multiple sound speeds: a model of multiple DBI type actions and non-Gaussianities

TL;DR

This work extends inflationary theory to multi-speed scenarios by modeling two DBI-type scalar sectors with independent sound speeds. It develops a generalized adiabatic/isocurvature decomposition suitable for multiple and analyzes linear perturbations using the ADM formalism, showing that perturbations freeze at the maximum sound horizon . In the two-DBI model, the background and perturbation spectra are computed, revealing nearly scale-invariant curvature and entropy perturbations with tilts and , while entropy can be enhanced if one mass is light. Non-Gaussianities exhibit a dominant equilateral component governed by the smallest , and a potentially large local component when entropy perturbations convert to curvature during late inflation, especially in cascade-like evolution. These results situate multi-speed inflation as a viable extension of N-flation and curvaton-type scenarios, with distinctive observational signatures in non-Gaussianity patterns.

Abstract

In this letter we study adiabatic and isocurvature perturbations in the frame of inflation with multiple sound speeds involved. We suggest this scenario can be realized by a number of generalized scalar fields with arbitrary kinetic forms. These scalars have their own sound speeds respectively, so the propagations of field fluctuations are individual. Specifically, we study a model constructed by two DBI type actions. We find that the critical length scale for the freezing of perturbations corresponds to the maximum sound horizon. Moreover, if the mass term of one field is much lighter than that of the other, the entropy perturbation could be quite large and so may give rise to a growth outside sound horizon. At cubic order, we find that the non-Gaussianity of local type is possibly large when entropy perturbations are able to convert into curvature perturbations. We also calculate the non-Gaussianity of equilateral type approximately.

Paper Structure

This paper contains 12 sections, 71 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The model
  3. Linear perturbations
  4. ADM formalism and the action at quadratic order
  5. Curvature perturbations and isocurvature perturbations
  6. A model of two DBI type actions
  7. Background equations
  8. Quantum fluctuations and power spectrum
  9. Non-Gaussianities
  10. Equilateral type
  11. Local type
  12. Conclusion and discussions

Figures (1)

  • Figure 1: The plot of spectral indices as functions of the e-folding number ${\cal N}$ for curvature and entropy perturbations. The red solid line denotes the spectral index of curvature perturbation; the yellow dashed line denotes the spectral index of entropy perturbation. The background parameters are taken as: $\lambda_1=\lambda_2=10^{14},~m_1=10^{-6},~m_2=5\times10^{-6}$.