Non-Gaussianity, Spectral Index and Tensor Modes in Mixed Inflaton and Curvaton Models

TL;DR

This work analyzes how fluctuations from both the inflaton and a curvaton can shape primordial density perturbations, focusing on non-Gaussianity, the scalar spectral index, and tensor modes. They solve for observables using a delta-N framework, deriving expressions for the power spectrum, n_s, n_run, r, and the nonlinearity parameters f_NL, tau_NL, and g_NL, with analytic limits and numerical results applied to chaotic, new, and hybrid inflation. A key finding is that large non-Gaussianity can arise even when curvaton contributions are subdominant, and the curvaton can liberate some inflation models by modifying n_s and r, while also predicting distinctive trispectrum signatures and consistency relations. The results provide a systematic toolkit for testing mixed inflaton-curvaton scenarios against current data and emphasize the potential of trispectrum measurements for distinguishing models. This has significant implications for inflation-model building and future CMB analyses.

Abstract

We study non-Gaussianity, the spectral index of primordial scalar fluctuations and tensor modes in models where fluctuations from the inflaton and the curvaton can both contribute to the present cosmic density fluctuations. Even though simple single-field inflation models generate only tiny non-Gaussianity, if we consider such a mixed scenario, large non-Gaussianity can be produced. Furthermore, we study the inflationary parameters such as the spectral index and the tensor-to-scalar ratio in this kind of models and discuss in what cases models predict the spectral index and tensor modes allowed by the current data while generating large non-Gaussianity, which may have many implications for model-buildings of the inflationary universe.

Figures (13)

• Figure 1: Plots of $Q$ (top left), $Q_\sigma,$ (top right), $Q_{\sigma \sigma}$ (bottom right) and $Q_{\sigma \sigma \sigma}$ (bottom left) as functions of $\sigma_\ast$ for the cases with $s=10^{-4}$ (red solid line), $s=10^{-8}$ (blue dotted line) and $s=10^{-12}$ (green dashed line). Notice that $Q_{\sigma \sigma}$ and $Q_{\sigma \sigma \sigma}$ can be negative. When the functions take a negative value, the absolute value is drawn with a thin line. $\sigma_*$ is shown in units of $M_{\rm pl}$.
• Figure 2: Contours of the $e$-folding number $N$ in the $s$--$\sigma_\ast$ plane. Here we assumed the chaotic inflation model with $n=4$ for concreteness. $\sigma_*$ is shown in units of $M_{\rm pl}$.
• Figure 3: Contours of the ratio of the contribution from the curvaton fluctuation and the inflaton fluctuation $\zeta_{\rm cur}^2/ \zeta_{\rm inf}^2$ are shown in the $s$--$\sigma_\ast$ plane. Here we assumed the chaotic inflation model with $n=4$ for concreteness. For reference, we also show contours of $p$ which enables us to see the region where an analytic expression is valid provided in the previous section.
• Figure 4: 1$\sigma$ and 2$\sigma$ allowed contours from WMAP3 alone are shown, which is generated from the chain provided in the webpage LAMBDA.
• Figure 5: Contours of $n_s$ (left panel) and $r$ (right panel) in the $s$--$\sigma_\ast$ plane for the chaotic inflation model with $n=2$. In the absence of the curvaton contribution, the spectral index and the tensor-to-scalar ratio are $n_s=0.967$ and $r=0.133$ for $N_{\rm inf}=60.3$.