Quantum conformal fluctuations in a singular space-time

Abstract

The cosmological solutions of Einstein's general relativistic equations lead inevitably to space–time singularities1. However, general relativity is only an approximation to a fully quantized theory of gravity and we need to consider whether singularity persists in the quantum domain. Although a full quantum theory of gravity has not yet been developed, we show here that the above question can be tackled in a simplified model where only the conformal degree of freedom is quantized. Previous applications of this technique had shown that in specific cases the quantum conformai fluctuations (QCF) from the classical solutions diverge at the classical singularity, thus rendering the classical solution physically meaningless²,³. Recently one of us (J.V.N. ref. 4) has generalized this result to cover all dust cosmologies. Here we show that this conclusion is applicable to even more general types of cosmological singularities.