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.
