Non-Gaussianity from resonant curvaton decay

TL;DR

This work investigates curvature perturbations generated when a curvaton decays nonperturbatively via parametric resonance into another scalar field. Because the end-stage dynamics are highly nonlinear, standard perturbative decay calculations fail, prompting the authors to combine the delta N formalism with three-dimensional lattice field theory simulations within the separate-universe framework. They demonstrate that the resulting curvature perturbations are strongly non-Gaussian and not adequately captured by a local f_NL expansion for the parameter choices examined. The study highlights that resonant curvaton decay can imprint a substantial, highly nonlinear signature on primordial perturbations and motivates broader exploration of parameter space and decay channels in nonperturbative curvaton scenarios.

Abstract

We calculate curvature perturbations in the scenario in which the curvaton field decays into another scalar field via parametric resonance. As a result of a nonlinear stage at the end of the resonance, standard perturbative calculation techniques fail in this case. Instead, we use lattice field theory simulations and the separate universe approximation to calculate the curvature perturbation as a nonlinear function of the curvaton field. For the parameters tested, the generated perturbations are highly non-Gaussian and not well approximated by the usual fNL parameterisation. Resonant decay plays an important role in the curvaton scenario and can have a substantial effect on the resulting perturbations.

Figures (4)

• Figure 1: Evolution of the fields during one simulation run. To the left of the vertical dashed line the evolution is calculated with (\ref{['sigma_eq_motion_hom']})-(\ref{['equ:pressureint_hom']}); to the right it is calculated with (\ref{['sigma_eq_motion_conf']})-(\ref{['equ:pressureint_conf']}). The $\phi$ field is included as a homogeneous radiation component.
• Figure 2: The matter fraction $r$ during one simulation. The resonance is rapid and destroys $\sim 95\%$ of the matter. The two solid lines show the two definitions of $r$ given in (\ref{['equ:rpressure']}) and (\ref{['equ:rscalefactor']}). $\rho_{\rm ref}=5\times 10^{-23}$ is marked by the vertical dashed line. The blue dashed line represents the approximation (\ref{['rho_split']}) taken about this $\rho_{\rm ref}$
• Figure 3: Results from simulations for different ranges of $\sigma_0$ centred around $\overline{\sigma_0}=0.0005M_{\rm Pl}$, $\overline{\sigma_0}=0.001M_{\rm Pl}$ and $\overline{\sigma_0}=0.002M_{\rm Pl}$, each covering the values present in one Hubble volume today. The top and bottom rows show $\ln a_{\rm ref}$ and $r_{\rm ref}$ respectively measured at $\rho=5\times 10^{-23}M_{\rm Pl}^4$ and averaged over $10-50$ runs. The solid lines show quadratic fits of the form (\ref{['equ:fitfunction']}). The centre panels also show some numerical checks of the simulation results. The green (square) points represent simulations with time-steps double the length of the black points. The blue (diamond) points are represent a four times longer time-step. It can be seen that the results are within the errors of the primary runs.
• Figure 4: The curvature perturbation (\ref{['equ:deltan']}) as a function of the curvaton field value for the three cases (from top to bottom) $\overline{\sigma_0}=0.0005M_{\rm Pl},~0.001M_{\rm Pl},~0.002M_{\rm Pl}$, calculated using (\ref{['equ:zetaresult']}) with the value of $r_{\rm decay}$ taken from table \ref{['tab:fNL']}. In each case, the dependence is highly nonlinear, implying strong non-Gaussianity.