Applications To Cosmology
Misner hoped that the chaos would churn up and smooth out the early universe. Also, during periods in which one direction was static (e.g., going from expansion to contraction) formally the Hubble horizon in that direction is infinite, which he suggested meant that the horizon problem could be solved. Since the directions of expansion and contraction varied, presumably given enough time the horizon problem would get solved in every direction.
While an interesting example of gravitational chaos, it is widely recognized that the cosmological problems the Mixmaster universe attempts to solve are more elegantly tackled by cosmic inflation. The metric Misner studied is also known as the Bianchi type IX metric.
Read more about this topic: Mixmaster Universe