A numerical study of non-gaussianity in the curvaton scenario

TL;DR

The paper develops a numerical, gauge-invariant second-order perturbation framework for a two-fluid curvaton model, solving the background and perturbation equations to quantify non-Gaussianity through $f_{ m{NL}}$ on large scales. It benchmarks the results against the analytical sudden decay approximation, finding strong agreement for large curvaton energy density at decay and up to ~10% differences for small densities, highlighting the regime where the sudden-decay picture remains valid. By connecting the perturbative approach with the $ abla N$ formalism and introducing transfer parameters $r_1$ and $r_2$, the work clarifies how initial curvaton fluctuations map to the final curvature perturbation and its nonlinearity. The findings are consistent with current observational bounds (e.g., WMAP) and delineate how evolving curvaton amplitudes or future data could refine or constrain curvaton-based models of the early universe.

Abstract

We study the curvaton scenario using gauge-invariant second order perturbation theory and solving the governing equations numerically. Focusing on large scales we calculate the non-linearity parameter f_nl in the two-fluid curvaton model and compare our results with previous analytical studies employing the sudden decay approximation. We find good agreement of the two approaches for large curvaton energy densities at curvaton decay, Omega_dec, but significant differences of up to 10 percent for small Omega_dec.

Figures (9)

• Figure 1: Evolution of the normalised background curvaton density, $\Omega_{0\sigma}$, and the normalised decay rate $g$, as a function of the number of e-foldings, starting with initial density and decay rate $\Omega_{0\sigma}=10^{-2}$ and $\Gamma/H=10^{-3}$, corresponding to $p_{\rm{in}}=0.32$ on the left panel, and on the right panel with $\Gamma/H=10^{-6}$, corresponding to $p_{\rm{in}}=10$.
• Figure 2: Evolution of the total curvature perturbation, $\zeta_1$, and the normalised density perturbations at first order as a function of the number of e-foldings, starting with $\zeta_{1\sigma}=1$ and initial density and decay rate $\Omega_{0\sigma}=10^{-2}$ and $\Gamma/H=10^{-3}$, corresponding to $p_{\rm{in}}=0.32$.
• Figure 3:
• Figure 4: Evolution of the total curvature perturbation, $\zeta_2$, and the normalised density perturbations at second order as a function of the number of e-foldings, with initially $\zeta_{1\sigma,\rm{in}}=1$ and density and decay rate $\Omega_{0\sigma}=10^{-2}$ and $\Gamma/H=10^{-3}$, corresponding to $p_{\rm{in}}=0.32$.
• Figure 5: Same as Fig. \ref{['pix5']} but with $\Gamma/H=10^{-6}$ initially, corresponding to $p_{\rm{in}}=10$.