Relativistic Gross-Pitaevskii equation and the cosmological Bose Einstein Condensation

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.