  In the eternally inflationary background driven by the metastable vacua of
the landscape, it is possible that some local quantum fluctuations with the
null energy condition violation can be large enough to stride over the barriers
among different vacua, so that create some islands full of radiation in new
vacua, and then these emergently thermalized islands will enter into the
evolution of standard big bang cosmology. In this paper, we calculate the
spectrum of curvature perturbation generated during the emergence of island. We
find that generally the spectrum obtained is nearly scale invariant, which can
be well related to that of slow roll inflation by a simple duality. This in
some sense suggests a degeneracy between their scalar spectra. In addition, we
also simply estimate the non-Gaussianity of perturbation, which is naturally
large, yet, can lie well in the observational bound. The results shown here
indicate that the island emergently thermalized in the landscape can be
consistent with our observable universe.
