Minisuperspace Quantum Cosmology from the Einstein-Cartan Path Integral

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.

References in corpus (3)

• Asymptotics and Hamiltonians in a First order formalism
• Chiral vacuum fluctuations in quantum gravity
• Inflationary tensor fluctuations, as viewed by Ashtekar variables and their imaginary friends

Cited by in corpus (8)

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• Lorentzian quantum cosmology with torsion
• Unimodular Plebański Gravity
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• Relational Time as a Stochastic Variable in ADM Gravity
• Unimodular Proca Theory: Breaking the U(1) gauge symmetry of unimodular gravity via a mass term
• Unimodular time in JT gravity: a holographic clock