  Our universe experienced the accelerated expansion at least twice; an extreme
inflationary acceleration in the early universe and the recent mild
acceleration. By introducing the Bose-Einstein condensation (BEC) phase of a
boson field, we have been developing a unified model of dark energy (DE) and
dark matter (DM) for the later mild acceleration. In this scenario, two phases
of BEC (=DE) and normal gas (=DM) transform with each other through BEC phase
transition. This unified model has successfully explained the mild acceleration
as an attractor. We extend this BEC cosmology to the early universe without
introducing new ingredients. In this scenario, the inflation is naturally
initiated by the condensation of the bosons in the huge vacuum energy. This
inflation and even the cosmic expansion eventually terminates exactly at zero
energy density. We call this stage as stagflation. At this stagflation era,
particle production and the decay of BEC take place. The former makes the
universe turn into the standard hot big bang stage and the latter makes the
cosmological constant vanishingly small after the inflation. Furthermore, we
calculate the density fluctuations produced in this model, which turns out to
be in the range allowed by the present observational data. We also show that
the stagflation is quite robust and easily appears when one allows negative
region of the potential. Further, we comment on the possibility that BEC
generation/decay series might have continued all the time in the cosmic history
from the inflation to present.
