Temporal enhancement of super-horizon curvature perturbations from decays of two curvatons and its cosmological consequences

If more than one curvaton dominate the Universe at different epochs from each other, curvature perturbations can be temporarily enhanced to a value much larger than the observed one 10^{-5}. The traces of the enhancement may be left as higher order correlation functions, that is, as non-Gaussianity, the stochastic gravitational waves that are sourced by scalar-scalar mode couplings, as well as the primordial black holes that are formed by the gravitational collapse of the enhanced curvature perturbations. We first confirm that such a temporal enhancement indeed occurs by solving the linearized perturbation equations both numerically and analytically. We then derive an analytic expression of the full-order curvature perturbation which does not rely on the frequently used sudden decay approximation and is exact on super-horizon scales. By using this analytic formula, we provide expressions of the non-linearity parameters f_nl, tau_nl and g_nl. If both two curvatons contribute to the final curvature perturbations, the strong non-Gaussianity appears in the trispectrum rather than in the bispectrum. We also find a unique consistency relation between tau_nl and g_nl without f_nl. By using the second-order perturbation theory, we numerically show that the spectrum of the induced gravitational waves has a plateau corresponding to duration of the enhancement and such gravitational waves can be probed by ultimate-DECIGO and space-based atomic interferometers. We finally calculate the abundance of the primordial black holes and put a constraint on the amplitude of the enhanced curvature perturbations.