Island cosmology in the landscape

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 in the observational bound well. The results shown here indicate that the island emergently thermalized in the landscape can be consistent with our observable universe.