Smooth Bounce in Affine Quantization of Bianchi I

Abstract

We present the affine coherent state quantization of the Bianchi I model. As in our previous paper on quantum theory of Friedmann models, we employ a variable associated with a perfect fluid to play a role of clock. Then we deparameterize the model. A distinctive feature, absent in isotropic models, is an extra non-holonomic constraint, which survives the deparameterization and constrains the range of physical variables. The appearance of the constraint reflects the `amplification' of singularity due to anisotropy. The quantization smoothes the extra constraint and allows quantum contracting trajectories to be smoothly transformed into expanding ones. Making use of affine coherent state we develop a semiclassical description. Figures are included to illustrate our result.