Abstract
We show that the second accelerating expansion of the universe appears smoothly from the decelerating phase, which follows the initial inflation, in the two-dimensional soluble semiclassical dilaton gravity along with the modified Poisson brackets with noncommutativity between the relevant fields. This is in contrast to the fact that the ordinary solution of the equations of motion following from the conventional Poisson algebra describes a permanent accelerating universe without any phase change. In this modified model, it turns out that the noncommutative Poisson algebra is responsible for the remarkable phase transition to the second accelerating expansion.
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