  Recently, it has been showed that a slow expansion, which is asymptotically a
static state in infinite past and may be described as an evolution with
\epsilon \ll -1, of early universe may lead to the generation of primordial
perturbation responsible for the structure formation of observable universe.
However, its feasibility depends on whether the growing mode of Bardeen
potential before phase transition can be inherited by the constant mode of
curvature perturbation after phase transition. In this note, we phenomenally
regard this slow expansion as that driven by multi NEC violating scalar fields.
We calculate the curvature perturbation induced by the entropy perturbation
before phase transition, and find that the spectrum is naturally scale
invariant with a slight red tilt. The result has an interesting similarity to
that of slow roll inflation.
