Dissipative quantum systems such as an unstable field, thermal field, and cosmological particle production are investigated. Equations of motion for each appropriate mean field are revealed to be Langevin type. The derived correlation of the random field turns out not to be Gaussian nor white in general. A relation between a popular quantum average and the statistical correlation is also clarified.

We develop our novel model of cosmology based on the Bose-Einstein condensation. This model unifies the Dark Energy and the Dark Matter, and predicts multiple collapse of condensation, followed by the final acceleration regime of cosmic expansion. We first explore the generality of this model, especially the constraints on the boson mass and condensation conditions. We further argue the robustness of this model over the wide range of parameters of mass, self coupling constant and the condensation rate. Then the dynamics of BEC collapse and the preferred scale of the collapse are studied. Finally, we describe possible observational tests of our model, especially, the periodicity of the collapses and the gravitational wave associated with them.On the other hand, cosmic evolution has the same temperature dependence since the matter dominant universe behaves, in an adiabatic process, as ρ ∝ T 3/2 .(1 . 2) typeset using PTPT E X.cls Ver.0.9 * ) This constraint will be somewhat reduced later. See Eq.(32) * ) This is somewhat generalized later in section 3.2. * ) This exponentially decreasing amplitude of the balance may lead to the instability of the inflationary regime and the autonomous termination of this regime, given some small external perturbations.

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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.PACS numbers: 98.80.Cq,95.36.+x,95.35.+d