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If more than one curvaton dominate the Universe at different epochs from eachother, curvature perturbations can be temporarily enhanced to a value muchlarger than the observed one 10^{-5}. The traces of the enhancement may be leftas higher order correlation functions, that is, as non-Gaussianity, thestochastic gravitational waves that are sourced by scalar-scalar modecouplings, as well as the primordial black holes that are formed by thegravitational collapse of the enhanced curvature perturbations. We firstconfirm that such a temporal enhancement indeed occurs by solving thelinearized perturbation equations both numerically and analytically. We thenderive an analytic expression of the full-order curvature perturbation whichdoes not rely on the frequently used sudden decay approximation and is exact onsuper-horizon scales. By using this analytic formula, we provide expressions ofthe non-linearity parameters f_nl, tau_nl and g_nl. If both two curvatonscontribute to the final curvature perturbations, the strong non-Gaussianityappears in the trispectrum rather than in the bispectrum. We also find a uniqueconsistency relation between tau_nl and g_nl without f_nl. By using thesecond-order perturbation theory, we numerically show that the spectrum of theinduced gravitational waves has a plateau corresponding to duration of theenhancement and such gravitational waves can be probed by ultimate-DECIGO andspace-based atomic interferometers. We finally calculate the abundance of theprimordial black holes and put a constraint on the amplitude of the enhancedcurvature perturbations.

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