Scaling Functions for Baby Universes in Two-Dimensional Quantum Gravity

Abstract

We apply the recently proposed transfer matrix formalism to 2-dimensional quantum gravity coupled to $(2, 2k-1)$ minimal models. We find that the propagation of a parent universe in geodesic (Euclidean) time is accompanied by continual emission of baby universes and derive a distribution function describing their sizes. The $k\to \infty~ (c\to -\infty)$ limit is generally thought to correspond to classical geometry, and we indeed find a classical peak in the universe distribution function. However, we also observe dramatic quantum effects associated with baby universes at finite length scales.