Curvature and isocurvature perturbations in a three-fluid model of curvaton decay

TL;DR

We address the evolution of cosmological perturbations in a curvaton model where the curvaton decays into radiation and CDM, requiring a three-fluid treatment. By solving the background and perturbed equations, we derive a single transfer coefficient $r(p)$ that maps the initial curvaton perturbation $\zeta_{\sigma,\rm in}$ to the late-time radiation perturbation $\zeta_{\gamma,\rm out}$, while CDM inherits $\zeta_{\rm m,out}=\zeta_{\sigma,\rm in}$. The final isocurvature isocurvature perturbation is $\mathcal{S}_{m\gamma}=3(1-r)\,\zeta_{\sigma,\rm in}$, with an exact relation $\mathcal{S}/\zeta|_{\rm nuc}=3(1-r)/r$ that holds beyond the sudden-decay approximation. The work connects CMB constraints to curvaton decay parameters through the scale-independent transfer function $r(p)$ and highlights how a CDM component produced from curvaton decay yields a fixed, correlated isocurvature signature and a realizable route to probe non-Gaussianity via $f_{\rm NL} \approx 5/(4r)$ for small $r$.

Abstract

We study the evolution of the cosmological perturbations after inflation in curvaton models where the non-relativistic curvaton decays into both radiation and a cold dark matter component. We calculate the primordial curvature and correlated isocurvature perturbations inherited by the radiation and cold dark matter after the curvaton has decayed. We give the transfer coefficient in terms of the initial curvaton density relative to the curvaton decay rate.

Figures (8)

• Figure 1: The phase plot shows the evolution of the dimensionless energy density, $\Omega_\sigma$, for different values of the dimensionless parameter, p, defined in Eq. (\ref{['eq:defp']}), varying from $3.15\times10^{3}$ (top line) to $3.15\times10^{-3}$ (bottom line). For all of the lines $\Gamma_2\ll\Gamma_1$. The evolution of the densities of all three fluids are plotted below in Figs. \ref{['omeg_A']} to \ref{['omeg_C']} for the trajectories, marked A, B and C.
• Figure 2: (a) The evolution of $\Omega_\sigma$ (solid), $\Omega_\gamma$ (dashed) and $\Omega_{\rm{m}}$ (dotted) against e-foldings $N$ of line A of Fig.\ref{['fig1']}. The initial value of $\Omega_\sigma$ is $10^{-2.5}$, and $\Gamma_1=10^{-10}$ and $\Gamma_2=10^{-12}$. (b) The evolution of $\zeta_\sigma/\zeta_{\sigma {\hbox{\scriptsize ,in}}}$ (dotted), $\zeta_\gamma/\zeta_{\sigma {\hbox{\scriptsize ,in}}}$ (dot--dashed), $\zeta_{\rm{m}}/\zeta_{\sigma {\hbox{\scriptsize ,in}}}$ (dashed) and the total curvature perturbation, $\zeta/\zeta_{\sigma {\hbox{\scriptsize ,in}}}$ (solid), against e-foldings $N$ of line A of Fig.\ref{['fig1']}.
• Figure 3: (a) The evolution of $\Omega_\sigma$ (solid), $\Omega_\gamma$ (dashed) and $\Omega_{\rm{m}}$ (dotted) against e-foldings $N$ of line B of Fig.\ref{['fig1']}. The initial value of $\Omega_\sigma$ is $10^{-4.6}$. $\Gamma_1$ and $\Gamma_2$ are the same as in Fig.\ref{['omeg_A']}. (b) The evolution of $\zeta_\sigma/\zeta_{\sigma {\hbox{\scriptsize ,in}}}$ (dotted), $\zeta_\gamma/\zeta_{\sigma {\hbox{\scriptsize ,in}}}$ (dot--dashed), $\zeta_{\rm{m}}/\zeta_{\sigma {\hbox{\scriptsize ,in}}}$ (dashed) and the total curvature perturbation, $\zeta/\zeta_{\sigma {\hbox{\scriptsize ,in}}}$ (solid), against e-foldings $N$ of line B of Fig.\ref{['fig1']}.
• Figure 4: (a) The evolution of $\Omega_\sigma$ (solid), $\Omega_\gamma$ (dashed) and $\Omega_{\rm{m}}$ (dotted) against e-foldings $N$ of line C of Fig.\ref{['fig1']}. The initial value of $\Omega_\sigma$ is $10^{-5.5}$. $\Gamma_1$ and $\Gamma_2$ are the same as in Fig.\ref{['omeg_A']}. (b) The evolution of $\zeta_\sigma/\zeta_{\sigma {\hbox{\scriptsize ,in}}}$ (dotted), $\zeta_\gamma/\zeta_{\sigma {\hbox{\scriptsize ,in}}}$ (dot--dashed), $\zeta_{\rm{m}}/\zeta_{\sigma {\hbox{\scriptsize ,in}}}$ (dashed) and the total curvature perturbation, $\zeta/\zeta_{\sigma {\hbox{\scriptsize ,in}}}$ (solid), against e-foldings $N$ of line C of Fig.\ref{['fig1']}.
• Figure 5: The evolution of the density perturbations on uniform-curvature hypersurfaces, $\delta\rho_\sigma$ (solid), $\delta\rho_\gamma$ (dashed) and $\delta\rho_{\rm{m}}$ (dotted), against e-foldings $N$ along the background trajectory B in Fig.\ref{['fig1']}.