  We study cosmological phase transitions from modified equations of motion by
introducing two non-commutative parameters in the Poisson brackets, which
describes the initial- and future-singularity-free phase transition in the
soluble semi-classical dilaton gravity with a non-vanishing cosmological
constant. Accelerated expansion and decelerated expansion corresponding to the
FRW phase appear alternatively, and then it ends up with the second accelerated
expansion. The final stage of the universe approaches the flat spacetime
independent of the initial state of the curvature scalar as long as the product
of the two non-commutative parameters is less than one. Finally, we show that
the initial-singularity-free condition is related to the second accelerated
expansion of the universe.
