Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2000-07-22
Prog.Theor.Phys. 103 (2000) 893-905
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
13 pages and 5 figures
Scientific paper
10.1143/PTP.103.893
In the framework of the Hartle-Hawking no-boundary proposal, we investigated quantum creation of the multidimensional universe with a cosmological constant ($\Lambda$) but without matter fields. We have found that the classical solutions of the Euclidean Einstein equations in this model have ``quasi-attractors'', i.e., most trajectories on the a-b plane, where a and b are the scale factors of external and internal spaces, go around a point. It is presumed that the wave function of the universe has a hump near this quasi-attractor point. In the case that both the curvatures of external and internal spaces are positive, and $\Lambda>0$, there exist Lorentzian solutions which start near the quasi-attractor, the internal space remains microscopic, and the external space evolves into our macroscopic universe.
Ochiai Hirotaka
Sato Katsuhiko
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