Summing over Non-singular Paths in Quantum Cosmology

Abstract

In this paper we provide the DeWitt propagator and its wave function in quantum cosmology using the path integral formulation of quantum gravity. The DeWitt boundary condition is introduced as a way to avoid the Big Bang singularity by positing that the wave function of the universe vanishes near the Big Bang. However, there is currently no clear definition of the DeWitt boundary condition in the path integral formulation. To address this issue, we use the image method, which eliminates singular paths in the forbidden region of the infinite potential, and apply this method to quantum cosmology based on the Batalin-Fradkin-Vilkovisky formulation of the path integral. We investigate the validity of the image method, and in particular, find that this method is only appropriate when the potential has symmetry with respect to the boundary. We then show that the DeWitt propagator and the DeWitt wave function derived from the image method are consistent with solutions of the Wheeler-DeWitt equation for certain models of quantum cosmology.

24 pages, references added, published version

References in corpus (12)

• Quantum phantom cosmology
• No Rescue for the No Boundary Proposal
• The Real No-Boundary Wave Function in Lorentzian Quantum Cosmology
• Singularity avoidance for collapsing quantum dust in the Lemaitre-Tolman-Bondi model
• The No-Boundary Proposal as a Path Integral with Robin Boundary Conditions
• The no-boundary proposal in biaxial Bianchi IX minisuperspace
• A quantum cosmology approach to cosmic coincidence and inflation
• Dirac observables and boundary proposals in quantum cosmology
• No Smooth Spacetime in Lorentzian Quantum Cosmology and Trans-Planckian Physics
• DeWitt wave function in Hořava-Lifshitz cosmology with tensor perturbation
• On the relation between boundary proposals and hidden symmetries of the extended pre-big bang quantum cosmology
• DeWitt boundary condition in one-loop quantum cosmology