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 (14)

• Lorentzian Quantum Cosmology
• The quantization of unimodular gravity and the cosmological constant problem
• No smooth beginning for spacetime
• Tunneling wave function of the universe
• Unimodular loop quantum gravity and the problems of time
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• Asymptotics and Hamiltonians in a First order formalism
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• Cosmological time and the constants of nature
• Chiral vacuum fluctuations in quantum gravity
• The Wave Function of Simple Universes, Analytically Continued From Negative to Positive Potentials
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Cited by in corpus (8)

• Quantum cosmology of pure connection general relativity
• Unimodular Hartle-Hawking wave packets and their probability interpretation
• Lorentzian quantum cosmology with torsion
• Unimodular Plebański Gravity
• Evolution of the early universe in Einstein-Cartan theory
• 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