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.

We present the phase diagram, in both the microcanonical and the canonical ensemble, of the self-gravitating-ring (SGR) model, which describes the motion of equal point masses constrained on a ring and subject to 3D gravitational attraction. If the interaction is regularized at short distances by the introduction of a softening parameter, a global entropy maximum always exists, and thermodynamics is well defined in the mean-field limit. However, ensembles are not equivalent and a phase of negative specific heat in the microcanonical ensemble appears in a wide intermediate energy region, if the softening parameter is small enough. The phase transition changes from second to first order at a tricritical point, whose location is not the same in the two ensembles. All these features make of the SGR model the best prototype of a self-gravitating system in one dimension. In order to obtain the stable stationary mass distribution, we apply an iterative method, inspired by a previous one used in 2D turbulence, which ensures entropy increase and, hence, convergence towards an equilibrium state.