Radiation-dominated quantum Friedmann models

Journal Article · Fri Mar 01 04:00:00 EST 1996 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.531443· OSTI ID:282063

Lemos, N A ^[1]

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1. Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)

Radiation-filled Friedmann{endash}Robertson{endash}Walker universes are quantized according to the Arnowitt{endash}Deser{endash}Misner formalism in the conformal-time gauge. Unlike previous treatments of this problem, here both closed and open models are studied, only square-integrable wave functions are allowed, and the boundary conditions to ensure self-adjointness of the Hamiltonian operator are consistent with the space of admissible wave functions. It turns out that the tunneling boundary condition on the universal wave function is in conflict with self-adjointness of the Hamiltonian. The evolution of wave packets obeying different boundary conditions is studied, and it is generally proven that all models are nonsingular. Given an initial condition on the probability density under which the classical regime prevails, it is found that a closed universe is certain to have an infinite radius, a density parameter {Omega}=1 becoming a prediction of the theory. Quantum stationary geometries are shown to exist for the closed universe model, but oscillating coherent states are forbidden by the boundary conditions that enforce self-adjointness of the Hamiltonian operator. {copyright} {ital 1996 American Institute of Physics.}

• DOE Contract Number: FC02-94ER40818
• OSTI ID: 282063
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 3 Vol. 37; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
BOUNDARY CONDITIONS
COHERENT STATES
COSMOLOGICAL MODELS
GRAVITATIONAL FIELDS
HAMILTONIANS
QUANTIZATION
QUANTUM GRAVITY
WAVE FUNCTIONS