  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.
