Simple model of big-crunch/big-bang transition
  We present classical and quantum dynamics of a test particle in the compactified Milne space. Background spacetime includes one compact space dimension undergoing contraction to a point followed by expansion. Quantization consists in finding a self-adjoint representation of the algebra of particle observables. Our model offers some insight into the nature of the cosmic singularity. 
Przemyslaw Malkiewicz and Wlodzimierz Piechocki