Wave function of the Universe and Chern-Simons Perturbation Theory

TL;DR

This paper presents an exact solution for the wave function of the universe in quantum gravity using Chern-Simons theory, including perturbative expansion and implications for cosmology.

Contribution

It introduces a novel exact solution for the wave function of the universe in four-dimensional quantum gravity via Chern-Simons theory with sources.

Findings

Wave function computed for a 3-sphere topology

State remains well-defined at degenerate dreibein values

Discusses relevance to cosmological models

Abstract

The Chern-Simons exact solution of four-dimensional quantum gravity with nonvanishing cosmological constant is presented in metric variable as the partition function of a Chern-Simons theory with nontrivial source. The perturbative expansion is given, and the wave function is computed to the lowest order of approximation for the Cauchy surface which is topologically a 3-sphere. The state is well-defined even at degenerate and vanishing values of the dreibein. Reality conditions for the Ashtekar variables are also taken into account; and remarkable features of the Chern-Simons state and their relevance to cosmology are pointed out.