Curvaton scenarios with inflaton decays into curvatons

We consider the possible decay of the inflaton into curvaton particles during reheating and analyze its effect on curvaton scenarios. Typical decay curvatons are initially relativistic then become nonrelativistic, changing the background history of the Universe. We show that this change to the background is the only way in which observational predictions of the scenario are modified. Moreover, once the required amplitude of perturbations is fixed by observation there are no signatures of such decays in other cosmological observables. The decay curvatons can prevent the Universe from becoming dominated by the curvaton condensate, making it impossible to match observations in parts of parameter space. This constrains the branching ratio of the inflaton to curvaton to be less than of order 0.1 typically. If the branching ratio is below about ${10}^{-4}$ it has negligible impact on the model parameter space and can be ignored.

Figure 1

Observational constraints in the case without inflaton-to-curvaton decays, updating the constraints we presented in Ref. [8]. The upper horizontal plane is the limit from $r$, the bottom near-horizontal surface is from $n_{\mathrm{s}}$, the left-hand surface from $f_{\mathrm{NL}}$ and the right-hand surface the limit (via $r_{\mathrm{dec}}$ from the observed perturbation amplitude. The allowed region is the portion between these two sets of planes. The highest value of $m_{\varphi }$ shown corresponds to perturbations coming entirely from inflaton, though this is now excluded by the $r$ constraint.

Figure 2

A schematic of the main events, showing (on log scales) the evolution of the densities with scale factor. The timing of the various events is mostly given by the Hubble parameter equaling one of the model parameters. From left to right we have the end of inflation, curvaton oscillations beginning, the inflaton decaying, the decay curvatons becoming nonrelativistic, the decay curvatons reaching equality with decay radiation, and the decay of the curvatons (both condensate and inflaton-decay generated). The alternative sequence that we also consider puts curvaton oscillations beginning after inflaton decay, though still before NR.

Figure 3

Constraint plots for four different values of $f$, namely 0.1, 0.01, 0.001, and 0.0001. The original four constraint surfaces are as in Fig. 1. The new scoop-shaped surface (not present in the top-left plot as it is off the top of the region viewed) delineates the region where the decay curvatons prevent $r_{\mathrm{dec}}$ from reaching the value required to generate the observed amplitude of perturbations, i.e. $r_{\mathrm{dec}}^{\max }<r_{\mathrm{dec}}^{\text{observed}}$. The allowed region is above the scoop. This constraint surface replaces the previous right-hand surface, which we still show for comparison.