Primordial non-Gaussianity from G-inflation

TL;DR

This work extends single-field inflation by analyzing G-inflation, where the inflaton Lagrangian includes a Galileon-like term $G(\phi,X)\Box\phi$. The authors derive general, non-slow-roll expressions for the power spectrum and its tilt, showing how a nontrivial sound speed $c_s$ and the background parameters $\epsilon$, $s$, and $\delta$ shape scale-invariance. They compute the cubic action and use the in-in formalism to obtain the bispectrum, demonstrating that the non-Gaussian amplitude $f_{\rm NL}$ can be large when $c_s$ is small or when the parameter $\sigma$ is sizable, with predominantly equilateral-type shapes. The results are applicable to both kinetically and potential-driven realizations, and reveal that large $f_{\rm NL}$ can be compatible with a large tensor-to-scalar ratio $r$, providing broad observational implications for upcoming CMB and large-scale structure probes.

Abstract

We present a comprehensive study of primordial fluctuations generated from G-inflation, in which the inflaton Lagrangian is of the form $K(φ, X)-G(φ, X)\Boxφ$ with $X=-(\partialφ)^2/2$. The Lagrangian still gives rise to second-order gravitational and scalar field equations, and thus offers a more generic class of single-field inflation than ever studied, with a richer phenomenology. We compute the power spectrum and the bispectrum, and clarify how the non-Gaussian amplitude depends upon parameters such as the sound speed. In so doing we try to keep as great generality as possible, allowing for non slow-roll and deviation from the exact scale-invariance.

Figures (4)

• Figure 1: The non-Gaussian amplitude ${\cal A}(1,k_2/k_1, k_3/k_1)(k_2/k_1)^{-1}(k_3/k_1)^{-1}$ as a function of $k_2/k_1$ and $k_3/k_1$ for kinematicallly driven G-inflation. The amplitude is normalized to unity at an equilateral configuration, $k_2/k_1=k_3/k_1=1$. The parameters are given by $\sigma = 0.36$, $c_{\rm s} =0.03$, $\varrho=1$, and ${\cal I}/{\cal G}=1$, so that $r\simeq 0.17$. The size of non-Gaussianity is $f_{\rm NL}\simeq 210$.
• Figure 2: The non-Gaussian amplitude ${\cal A}(1,k_2/k_1, k_3/k_1)(k_2/k_1)^{-1}(k_3/k_1)^{-1}$ as a function of $k_2/k_1$ and $k_3/k_1$ for kinematicallly driven G-inflation. The amplitude is normalized to unity at an equilateral configuration, $k_2/k_1=k_3/k_1=1$. The parameters are given by $\sigma = 0.1$, $c_{\rm s} =0.1$, $\varrho=60$, and ${\cal I}/{\cal G}=1$. The size of non-Gaussianity is $f_{\rm NL}\simeq 204$.
• Figure 3: The non-Gaussian amplitude ${\cal A}(1,k_2/k_1, k_3/k_1)(k_2/k_1)^{-1}(k_3/k_1)^{-1}$ as a function of $k_2/k_1$ and $k_3/k_1$ for kinematicallly driven G-inflation. The amplitude is normalized to unity at an equilateral configuration, $k_2/k_1=k_3/k_1=1$. The parameters are given by $\sigma = 0.1$, $c_{\rm s} =0.1$, $\varrho=1$, and ${\cal I}/{\cal G}=300$. In this case the shape peaks in the folded configuration $k_1=2k_2=2k_3$.
• Figure 4: The non-Gaussian amplitude ${\cal A}(1,k_2/k_1, k_3/k_1)(k_2/k_1)^{-1}(k_3/k_1)^{-1}$ as a function of $k_2/k_1$ and $k_3/k_1$ for potential driven G-inflation. The amplitude is normalized to unity at an equilateral configuration, $k_2/k_1=k_3/k_1=1$. The size of non-Gaussianity is $f_{\rm NL}=235/3888\simeq 0.06$.