Transition from AdS universe to DS universe in the BPP model

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It can be shown that in the BPP model the smooth phase transition from the asymptotically decelerated AdS universe to the asymptotically accelerated DS universe is possible by solving the modified semiclassical equations of motion. This transition comes from noncommutative Poisson algebra, which gives the constant curvature scalars asymptotically. The decelerated expansion of the early universe is due to the negative energy density with the negative pressure induced by quantum back reaction, and the accelerated late-time universe comes from the positive energy and the negative pressure which behave like dark energy source in recent cosmological models.