Non-Gaussian Fingerprints of Self-Interacting Curvaton

TL;DR

The paper analyzes non-Gaussianities in self-interacting curvaton models with $V=\frac{1}{2}m^2\sigma^2+\lambda\sigma^{n+4}$, $n\in\{0,2,4,6\}$, using the $\Delta N$ formalism to connect initial curvaton fluctuations to the curvature perturbation $\zeta$. By numerically solving the coupled curvaton–radiation system and scanning parameter space, the authors compute $f_{\mathrm{NL}}$ and $g_{\mathrm{NL}}$ and identify regions consistent with observational bounds, revealing substantial deviations from quadratic predictions when self-interactions dominate. Self-interactions induce oscillations in $\zeta(\sigma_*)$, cause $f_{\mathrm{NL}}$ to cross zero, and can leave $g_{\mathrm{NL}}$ nonzero, thereby violating the usual relations $f_{\mathrm{NL}}\sim 1/r_{\mathrm{dec}}$ and $g_{\mathrm{NL}}\sim f_{\mathrm{NL}}^2$. The results show smoother parameter regions for renormalizable ($n=0$) potentials and patchy viable regions for non-renormalizable cases ($n=2,4$), highlighting how non-Gaussianity measurements can test curvaton self-interactions.

Abstract

We investigate non-Gaussianities in self-interacting curvaton models treating both renormalizable and non-renormalizable polynomial interactions. We scan the parameter space systematically and compute numerically the non-linearity parameters f_NL and g_NL. We find that even in the interaction dominated regime there are large regions consistent with current observable bounds. Whenever the interactions dominate, we discover significant deviations from the relations f_NL ~ 1/r_decay and g_NL ~ 1/r_decay valid for quadratic curvaton potentials, where r_decay measures the curvaton contribution to the total energy density at the time of its decay. Even if r_decay << 1, there always exists regions with f_NL ~ 0 since the sign of f_NL oscillates as a function of the parameters. While g_NL can also change sign, typically g_NL is non-zero in the low-f_NL regions. Hence, for some parameters the non-Gaussian statistics is dominated by g_NL rather than by f_NL. Due to self-interactions, both the relative signs of f_NL and g_NL and the functional relation between them is typically modified from the quadratic case, offering a possible experimental test of the curvaton interactions.

Figures (7)

• Figure 1: Contour plots of $f_{\rm NL}$ (left panel) and $g_{\rm NL}$ (right panel) with variables $r_{\mathrm{dec}}$ and $\sqrt{\lambda}\sigma_{*}/m$ as $x$ and $y$ axes, respectively. On the left panel, the contours run from $0$ (black) to $100$ (white) with spacing of $10$. On the right panel, they run with spacing of $500$ from $-5000$ (black) to $0$ (white).
• Figure 2: The behaviour of $|f_{\mathrm{NL}}|$ and $|g_{\mathrm{NL}}|$ for $n=4$ and $m=10^{-12}$.
• Figure 3: Magnitude of $|f_{\mathrm{NL}}|$ and $|g_{\mathrm{NL}}|$ for $n=4$ and $m=10^{-12}$.
• Figure 4: A schematical illustration of the different cuts limiting the allowed area in the parameter space.
• Figure 5: Dark areas correspond to the allowed areas in the parameter space with $-9 < f_{\mathrm{NL}} < 111$ and $-3.5\times10^5 < g_{\mathrm{NL}} < 8.2\times10^5$ for $n=0$ and $n=6$.