Size of a bouncing mixmaster universe

An analysis is given of the evolution of a massive scalar field in a closed mixmaster universe of Bianchi type IX. Although the scalar field violates the strong energy condition, the probability of the model "bouncing" at a very early time is infinitesimally small; of the order of the ratio of the minimum to maximum sizes of the universe ∼${10}^{-40\mathrm{}}$.