Cosmological singularity problem

Observational cosmology and known general relativity models of the Universe strongly suggest an existence of the initial cosmological singularity. The BKL scenario is thought to be a generic solution to the Einstein equations near the singularity. One believes that imposition of quantum rules onto this scenario may heal the singularity. Quantum BKL scenario could be used as a realistic model of the very early Universe. The Bianchi IX model underlies the BKL so its quantization should open the door to the quantization of the BKL. We present some preliminary analysis concerning this issue. First, we present the critical points of the dynamics of the Bianchi IX model which turn out to be of nonhyperbolic type, and are connected with chaotic dynamics of this model. Later, we quantize this model within adiabatic approximation. Quantization turns the classical singularity into quantum bounce. Afterwards, we discuss the statistics of the energy spectrum, which shows the level repulsion. It seems that quantization does not suppress the chaos. Finally, we outline prospects of this program.

M.Kowal, W.Piechocki, L.Roszkowski, J.Skalski