  The possibility that the universe may have a fundamental and positive
cosmological constant has motivated an interesting cosmological model, in which
initially the universe is in a cosmological constant sea, then the local
quantum fluctuations violating the null energy condition create some islands
with matter and radiation, which under certain conditions might corresponds to
our observable universe. We in this note study the perturbation spectra of
scalar fields not affecting the evolution of background during the fluctuation.
We will examine whether they can be interesting, and responsible for the
structure formation of observable universe.
