INITIAL SINGULARITY PROBLEM IN 2-DIMENSIONAL QUANTUM COSMOLOGY

The problem of how to put interactions in two-dimensional quantum grav ity in the strong coupling regime is studied. It shows that the most g eneral interaction consistent with this symmetry is a Liouville term t hat contains two parameters (alpha,beta) satisfying the algebraic rela tion 2 beta-alpha=2 in order to assure the closure of the diffeomorphi sm algebra. The model is classically soluble and it contains as a gene ral solution the temporal singularity. The theory is quantized and we show that the propagation amplitude falls to zero in tau=0. This resul t shows that the classical singularities are smoothed by quantum effec ts and the big-bang concept could be considered as a classical extrapo lation instead of a physical concept.