Scale-dependence of Non-Gaussianity in the Curvaton Model

TL;DR

This work investigates the scale‑dependence of non‑Gaussianity in a self‑interacting curvaton model by introducing a potential $V(\sigmaigr)= frac{1}{2} m_\sigma^2 \sigma^2 + \\lambda m_\sigma^4 ( frac{\sigma}{m_\sigma})^p$ with a self‑interaction strength $s$. It derives the bispectrum and trispectrum parameters $f_{ m NL}$ and $g_{ m NL}$ and their scale‑dependences $n_{f_{ m NL}}$ and $n_{g_{ m NL}}$, expressed through $V'''(\sigma_*)$, $V''(\sigma_*)$, and derivatives of the oscillating curvaton field. Numerically, $n_{f_{ m NL}}$ can reach values ~0.1 for certain $(p,s)$, suggesting potential observability by future CMB missions when $f_{ m NL}$ is in the detectable range; the sign of $f_{ m NL}$ and the breakdown of a simple power‑law description are also discussed. Furthermore, $g_{ m NL}$ and its scale‑dependence offer a complementary probe that can break degeneracies and, together with $f_{ m NL}$ and $n_{f_{ m NL}}$, may fix the model parameters, with $n_{g_{ m NL}}$ providing an additional diagnostic. Overall, the paper demonstrates that scale‑dependent non‑Gaussianity is a promising avenue to test self‑interacting curvaton scenarios and to potentially determine the origin of primordial perturbations with forthcoming data.

Abstract

We investigate the scale-dependence of f_NL in the self-interacting curvaton model. We show that the scale-dependence, encoded in the spectral index n_{f_NL}, can be observable by future cosmic microwave background observations, such as CMBpol, in a significant part of the parameter space of the model. We point out that together with information about the trispectrum g_NL, the self-interacting curvaton model parameters could be completely fixed by observations. We also discuss the scale-dependence of g_NL and its implications for the curvaton model, arguing that it could provide a complementary probe in cases where the theoretical value of n_{f_NL} is below observational sensitivity.

Figures (5)

• Figure 1: Plots of $n_{f_{\rm NL}}$ (left panel) and $f_{\rm NL}$ (right panel) as a function of the power $p$. Here we take $s=0.05$ (red line) and $0.07$ (green line) with $\eta_{\sigma\sigma}=0.005$. The shaded areas correspond to the regions where the power-law form $f_{\rm NL} \propto k^{n_{f_{\rm NL}}}$ does not hold.
• Figure 2: Contours of $f_{\rm NL}$ and $n_{f_{\rm NL}}$ for $p=6$ (left panel) and $8$ (right panel). The region with $f_{\rm NL} < 10$ is shaded.
• Figure 3: Regions testable in future observations. Shown is the parameter space where the theoretical prediction for $n_{f_{\rm NL}}$ exceeds $\Delta n_{f_{\rm NL}}$ given in Eq. \ref{['eq:nfNL_obs']}, (i.e., region where $n_{f_{\rm NL}} > \Delta n_{f_{\rm NL}} = 0.05 \times (50/f_{\rm NL})$ is satisfied), for $10 \le f_{\rm NL} \le 100$.
• Figure 4: Plots of $n_{f_{\rm NL}}$ (right) and $g_{\rm NL}$ (left) for the cases with $(p,s)=(6,0.0622)$ and $(8, 0.0214)$. The value of $s$ is chosen such that the cases of $p=6$ and $8$ give almost the same values of $n_{f_{\rm NL}}$ as a function of $f_{\rm NL}$.
• Figure 5: Plot of $n_{g_{\rm NL}}$ as a function of the power $p$ for $s=0.07$.