Probability distribution for the quantum universe

A bstract We determine the inner product on the Hilbert space of wavefunctions of the universe by imposing the Hermiticity of the quantum Hamiltonian in the context of the minisuperspace model. The corresponding quantum probability density reproduces successfully the classical probability distributi...

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Bibliographic Details
Published in:The journal of high energy physics 2021-12, Vol.2021 (12), p.1-16, Article 165
Main Authors: Kehagias, Alex, Partouche, Hervé, Toumbas, Nicolaos
Format: Article
Language:English
Subjects:
Big bang cosmology
Classical and Quantum Gravitation
Density
Elementary Particles
General Relativity and Quantum Cosmology
High energy physics
High Energy Physics - Theory
Hilbert space
Models of Quantum Gravity
Physics
Physics and Astronomy
Probability distribution
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
Singularities
Spacetime Singularities
String Theory
Universe
Wave functions
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Summary:A bstract We determine the inner product on the Hilbert space of wavefunctions of the universe by imposing the Hermiticity of the quantum Hamiltonian in the context of the minisuperspace model. The corresponding quantum probability density reproduces successfully the classical probability distribution in the ħ → 0 limit, for closed universes filled with a perfect fluid of index w . When − 1/3 < w ≤ 1, the wavefunction is normalizable and the quantum probability density becomes vanishingly small at the big bang/big crunch singularities, at least at the semiclassical level. Quantum expectation values of physical geometrical quantities, which diverge classically at the singularities, are shown to be finite.
ISSN:1029-8479
1126-6708
1029-8479
DOI:10.1007/JHEP12(2021)165