  We examine the possibility of dealing with gravitational singularities on a
quantum level through the use of coherent state or wavelet quantization instead
of canonical quantization. We consider the Robertson-Walker metric coupled to a
perfect fluid. It is the simplest model of a gravitational collapse and the
results obtained here may serve as a useful starting point for more complex
investigations in future. We follow a quantization procedure based on affine
coherent states or wavelets built from the unitary irreducible representation
of the affine group of the real line with positive dilation. The main issue of
our approach is the appearance of a quantum centrifugal potential allowing for
regularization of the singularity, essential self-adjointness of the
Hamiltonian, and unambiguous quantum dynamical evolution.
