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Primordial non-Gaussianity from the DBI Galileons

Shuntaro Mizuno, Kazuya Koyama

TL;DR

The paper develops a generalized DBI Galileon framework via a P(X,φ)−G(X,φ) action to study primordial fluctuations during inflation. It derives the power spectrum and a bispectrum that includes a novel Galileon-induced shape, showing the equilateral f_NL estimator remains a robust probe thanks to strong shape overlap. For DBI Galileons, f_NL^equil scales like 1/c_s^2 with bounds -0.32/c_s^2 < f_NL^equil < -0.16/c_s^2, while a near-b_D–independent relation links f_NL^equil to (1−n_s) and r; in G-inflation, f_NL^equil = 4.62 r^−2/3, imposing tight constraints from tensor mode measurements. Overall, the work highlights how Galileon terms modify inflationary predictions, including a broken consistency relation and enhanced non-Gaussianity for small sound speeds, with implications for string-theory embeddings and future observations.

Abstract

We study primordial fluctuations generated during inflation in a class of models motivated by the DBI Galileons, which are extensions of the DBI action that yield second order field equations. This class of models generalises the DBI Galileons in a similar way with K-inflation. We calculate the primordial non-Gaussianity from the bispectrum of the curvature perturbations at leading order in the slow-varying approximations. We show that the estimator for the equilateral-type non-Gaussianity, $f_{\rm NL} ^{equil}$, can be applied to measure the amplitude of the primordial bispectrum even in the presence of the Galileon-like term although it gives a slightly different momentum dependence from K-inflation models. For the DBI Galileons, we find $-0.32 /c_s^2 < f_{\rm NL} ^{equil} < -0.16/c_s^2$ and large primordial non-Gaussianities can be obtained when $c_s$ is much smaller than 1 as in the usual DBI inflation. In G-inflation models, where a de Sitter solution is obtained without any potentials, the non-linear parameter is given by $f_{\rm NL}^{equil} = 4.62 r^{-2/3}$ where $r$ is the tensor to scalar ratio, giving a stringent constraint on the model.

Primordial non-Gaussianity from the DBI Galileons

TL;DR

The paper develops a generalized DBI Galileon framework via a P(X,φ)−G(X,φ) action to study primordial fluctuations during inflation. It derives the power spectrum and a bispectrum that includes a novel Galileon-induced shape, showing the equilateral f_NL estimator remains a robust probe thanks to strong shape overlap. For DBI Galileons, f_NL^equil scales like 1/c_s^2 with bounds -0.32/c_s^2 < f_NL^equil < -0.16/c_s^2, while a near-b_D–independent relation links f_NL^equil to (1−n_s) and r; in G-inflation, f_NL^equil = 4.62 r^−2/3, imposing tight constraints from tensor mode measurements. Overall, the work highlights how Galileon terms modify inflationary predictions, including a broken consistency relation and enhanced non-Gaussianity for small sound speeds, with implications for string-theory embeddings and future observations.

Abstract

We study primordial fluctuations generated during inflation in a class of models motivated by the DBI Galileons, which are extensions of the DBI action that yield second order field equations. This class of models generalises the DBI Galileons in a similar way with K-inflation. We calculate the primordial non-Gaussianity from the bispectrum of the curvature perturbations at leading order in the slow-varying approximations. We show that the estimator for the equilateral-type non-Gaussianity, , can be applied to measure the amplitude of the primordial bispectrum even in the presence of the Galileon-like term although it gives a slightly different momentum dependence from K-inflation models. For the DBI Galileons, we find and large primordial non-Gaussianities can be obtained when is much smaller than 1 as in the usual DBI inflation. In G-inflation models, where a de Sitter solution is obtained without any potentials, the non-linear parameter is given by where is the tensor to scalar ratio, giving a stringent constraint on the model.

Paper Structure

This paper contains 8 sections, 52 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Model
  3. Power spectrum
  4. Bispectrum
  5. Examples
  6. The DBI Galileons
  7. G-inflation
  8. Conclusion

Figures (1)

  • Figure 1: In this group of figures, we plot the shape functions $F(1,k_2/k_1, k_3/k_1) (k_2/k_1)^2 (k_3/k_1)^2$ as functions of $(k_2/k_1, k_3/k_1)$. The figures are normalised to have values $1$ for equilateral configurations $k_2/k_1 = k_3/k_1 =1$ and set to zero outside the region $1-k_2/k_1 \leq k_3/k_1 \leq k_2/k_1$. We plot $F^{(1)} (k_1, k_2, k_3)$, $F^{(2)} (k_1, k_2, k_3)$, $F^{(3)}(k_1, k_2, k_3)$ and $F^{equil} (k_1, k_2, k_3)$ for upper left, upper right, lower left, lower right, respectively.