 Solution

After reheating, inflaton decay products are radiation with ${\rho }_{\gamma }\propto a^{-4}$, whereas the oscillating curvaton has ${\rho }_{\sigma }\propto a^{-3}$. Its fractional density therefore grows, so only the curvaton can become dynamically important at late times.

The curvaton mechanism can generate the observed primordial curvature perturbation even though the inflaton drives inflation. A viable pure-curvaton realization requires the field to be light during inflation, to become sufficiently important before decay, to decay into the visible sector before nucleosynthesis, and to avoid excessive residual isocurvature and primordial non-Gaussianity. If it dominates before complete decay, these conditions can be compatible with observations.