Multiple scalar particle decay and perturbation generation

TL;DR

This paper develops a model-independent analytic framework for the evolution of the early universe with multiple curvaton fields decaying into radiation and matter. Using a sudden-decay approximation, it derives closed-form transfer coefficients that map initial curvaton perturbations to final matter and radiation curvature perturbations, and it expresses the final isocurvature $\mathcal{S}_{m\gamma}$ in terms of these coefficients. The authors demonstrate excellent agreement with full numerical solutions across single, double, and multiple curvaton scenarios and show that the isocurvature signal crucially depends on decay branching ratios, precluding robust model-independent predictions. The results provide a quantitative bridge from multi-field curvaton dynamics to observable cosmological perturbations, with direct implications for CMB and large-scale-structure analyses.

Abstract

We study the evolution of the universe which contains a multiple number of non-relativistic scalar fields decaying into both radiation and pressureless matter. We present a powerful analytic formalism to calculate the matter and radiation curvature perturbations, and find that our analytic estimates agree with full numerical results within an error of less than one percent. Also we discuss the isocurvature perturbation between matter and radiation components, which may be detected by near future cosmological observations, and point out that it crucially depends on the branching ratio of the decay rate of the scalar fields and that it is hard to make any model independent predictions.

Figures (4)

• Figure 1: Plot of the integral $\int_0^{x_i}y \exp(-u_i) du_i$ versus $x\equiv x_1$. The value changes quickly only near the moment of decay time, $t\sim \Gamma^{-1}$, and becomes constant afterwards.
• Figure 2: The evolution of density parameters (upper row) and curvature perturbations (lower row) for three cases of two curvaton decays: as shown, the energy densities of the two curvaton fields are sub-dominant (left panel), dominant (right panel) and comparable (middle panel) to the radiation energy density. The details are given in Table \ref{['2curvatontable']}.
• Figure 3: The same as Fig. \ref{['2curvatongraph']} but with five curvaton fields. The details of the parameters are given in Table \ref{['multitable']}.
• Figure 4: All the parameters are the same as the right panel of Fig. \ref{['multigraph']} except the branching ratios to matter: here, $\Gamma_i^{(m)}/H^{\mathrm{(in)}}$ is given by $10^{-19}$, $10^{-17.5}$, $10^{-15}$, $10^{-13.5}$ and $10^{-11}$ for each curvaton, respectively. In this case, we have $\zeta_\gamma^{\mathrm{(out)}}/\zeta_1^{\mathrm{(in)}} = 0.956524$ ($\zeta_\gamma^{\mathrm{(out)}}/\zeta_1^{\mathrm{(in)}} = 0.950257$ with analytic approx.) and $\zeta_m^{\mathrm{(out)}}/\zeta_1^{\mathrm{(in)}} = 0.602384$, making $\mathcal{S}_{m\gamma}^{\mathrm{(out)}}$ not negligible.