Quantum fluctuations in gravitational collapse and cosmology

Abstract

It is shown that the conformal degrees of freedom in the metric tensor can be quantized and that this procedure leads to fluctuations around the solutions of the classical Einstein field equations. These fluctuations become progressively more important as the classical solution approaches the space-time singularity. An explicit calculation is given of the quantum mechanical propagator which describes the conformal fluctuations in a collapsing homogeneous ball of dust. As the state of classical singularity is approached the quantum uncertainty diverges. Within the range of quantum uncertainty non-singular final states are possible. The solution can also be applied to the Friedmann models with the conclusion that the Universe need not have originated in a unique classical big bang. Non-singular models or models without particle horizons are permitted within the range of the quantum uncertainty.