Towards quantum cosmology without singularities.

In this paper we investigate the vanishing of cosmological singularities by quantization. Starting from a 5d Kaluza{Klein approach we quantize, as a rst step, the non{spherical metric part and the dilaton eld. These elds which are classically singular become smooth after quantization. In addition, we argue that the incorporation of non perturbative quantum corrections form a dilaton potential. Technically, the procedure corresponds to the quantization of 2d dilaton gravity and we discuss several models. From the 4d point of view this procedure is a semiclassical approach where only the dilaton and moduli matter elds are quantized. We consider a cosmological string solution which has classical singularities (big bang). Near these singularities the theory factorizes in a smooth spherical part and a singular 2d part. This singular part is the well-known dilaton gravity (see e.g. [1]-[4]) and as a rst step we are going to quantize this part with the result that all singularities disappear. This procedure is also known as s-wave reduction and was so far used for 4d BH physics. 1. Classical theory. Our 4d classical model is given by S = Z dx q ~ Ge 2 R + 4(@ ) ( ) 1 12 H ! (1) where is a dilaton eld, H = @[ B ] is the torsion corresponding to the antisymmetric tensor eld B and is a modulus eld. A cosmological solution to this model is given Work supported by the Department of Energy, contract DE{AC03{76SF00515. e-mail: [email protected] e-mail: [email protected]