Quantum conformal cosmology

Abstract

This article discusses an approach to quantum gravity via path integrals. The more conventional approaches look upon general relativity as a field theory. It is argued here that relativity in fact seeks to replace the standard notion of force fields by the concept of non-Euclidean geometry. Any quantization program should take due note of this fundamental aspect. Here it is shown that considerable insight can be gained into the complexities of quantum gravity by a more limited but exact approach that quantizes the conformal degree of freedom only. It is shown, for example, that the likelihood of the universe having originated from a spacetime singularity is vanishingly small. Other interesting consequences of the approach are briefly described.