Minisuperspace Quantum Cosmology from the Einstein-Cartan Path Integral

TL;DR

This paper derives exact quantum cosmology propagators within the Einstein-Cartan framework using path integrals, revealing connections to Chern-Simons states and different boundary conditions without saddle point approximations.

Contribution

It provides a novel exact derivation of cosmological propagators from the Einstein-Cartan action, linking boundary conditions and contour choices to known quantum states.

Findings

Exact propagators derived without saddle point approximation.

Connection between boundary conditions and Chern-Simons states.

Unimodular propagators obtained straightforwardly.

Abstract

We derive the fixed-$\Lambda$ and unimodular propagators using the path integral formalism as applied to the Einstein-Cartan action. The simplicity of the action (which is linear in the lapse function) allows for an exact integration starting from the lapse function and the enforcement of the Hamiltonian constraint, leading to a product of Chern-Simons states if the connection is fixed at the endpoints. No saddle point approximation is needed. Should the metric be fixed at the endpoints, then, depending on the contour chosen for the connection, Hartle-Hawking or Vilenkin propagators are obtained. Thus, in this approach one trades a choice of contour in the lapse function for one in the connection, where appropriate. The unimodular propagators are also trivial to obtain via the path integral, and the previously derived expressions are recovered.