Quantization of closed mini-superspace models as bound states

Journal Article · Sun Jan 01 04:00:00 EST 1995 · General Relativity and Gravitation

DOI:https://doi.org/10.1007/BF02105672· OSTI ID:54558

Kung, J H ^[1]

---

1. Harvard-Smithsonian Center for Astrophysics, Cambridge, MA (United States)

The Wheeler-DeWitt equation is applied to closed k > 0 Friedmann-Robertson-Walker metric with various combinations of cosmological constant and matter (e.g., radiation or pressureless gas). It is shown that if the universe ends in the matter dominated era (e.g., radiation or pressureless gas) with zero cosmological constant, then the resulting Wheeler-DeWitt equation describes a bound state problem. As solutions of a non-degenerate bound state system, the eigen-wave functions are real (Hartle-Hawking). Furthermore, as a bound state problem, there exists a quantization condition that relates the curvature of the three space with the various energy densities of the universe. If one assumes that the universe is closed, then the quantum number of the universe is N {approximately} (Gk){sup {minus}1} {approximately} 10{sup 122}. The largeness of this quantum number is naturally explained by an early inflationary phase which resulted in the flat universe observed today. It is also shown that if there is a cosmological constant {Lambda} > 0 in the universe that persists for all time, then the resulting Wheeler-DeWitt equation describes a non-bound state system, regardless of the magnitude of the cosmological constant. As a consequence, the wave functions are in general complex (Vilenkin).

• Sponsoring Organization: USDOE
• OSTI ID: 54558
• Journal Information: General Relativity and Gravitation, Journal Name: General Relativity and Gravitation Journal Issue: 1 Vol. 27; ISSN 0001-7701; ISSN GRGVA8
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
MANY-DIMENSIONAL CALCULATIONS
MATHEMATICAL MODELS
QUANTIZATION
UNIVERSE