MIXMASTER UNIVERSE IN 4TH-ORDER GRAVITY THEORIES

We analyze the behavior of the Bianchi type-IX cosmological model in t he full fourth-order theory of gravity in four space-time dimensions o n approach to the singularity both analytically and numerically. By di rectly analyzing the full fourth-order field equations we prove explic itly that the Belinski-Khalatnikov-Lifshitz (BKL) analytic solution (a nd the accompanying bounce law) is also a solution to the more general case that we consider. But it appears to be nongeneric, because a per turbation analysis shows that power-law Kasner asymptotes are unstable on approach to the singularity. On the other hand, we find that the m odel possesses a stable isotropic monotonic power-law asymptotic solut ion and accordingly we show that there is a general solution which is nonchaotic near the space-time singularity. Numerical experiments conf irm the existence of such a behavior. The inclusion of matter fields d oes not alter the evolution in the neighborhood of the singularity. Th e role of space-time dimensionality on the chaotic evolution of the mi xmaster universe in these theories is also spelled out. In particular, we show that it is impossible to build a mixmaster universe in space- time dimensions higher than four in the full fourth-order gravity theo ry based on the BKL approximation scheme.