  We do not know 96% of the total matter in the universe at present. In this
paper, a cosmological model is proposed in which Dark Energy (DE) is identified
as Bose-Einstein Condensation (BEC) of some boson field. Global cosmic
acceleration caused by this BEC and multiple rapid collapses of BEC into black
holes etc. (=Dark Matter (DM)) are examined based on the relativistic version
of the Gross-Pitaevskii equation. We propose (a) a novel mechanism of inflation
free from the slow-rolling condition, (b) a natural solution for the cosmic
coincidence ('Why Now?') problem through the transition from DE into DM, (c)
very early formation of highly non-linear objects such as black holes, which
might trigger the first light as a form of quasars, and (d) log-z periodicity
in the subsequent BEC collapsing time. All of these are based on the steady
slow BEC process.
