Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2002-02-04
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Latex file, 15 pages, 2 figures
Scientific paper
In the isotropic quantum cosmological perfect fluid model, the initial singularity can be avoided, while the classical behaviour is recovered asymptotically. We verify if initial anisotropies can also be suppressed in a quantum version of a classical anisotropic model where gravity is coupled to a perfect fluid. Employing a Bianchi I cosmological model, we obtain a "Schr\"odinger-like" equation where the matter variables play de role of time. This equation has a hyperbolic signature. It can be explicitly solved and a wave packet is constructed. The expectation value of the scale factor, evaluated in the spirit of the many-worlds interpretation, reveals an isotropic Universe. On the other hand, the bohmian trajectories indicate the existence of anisotropies. This is an example where the Bohm-de Broglie and the many-worlds interpretations are not equivalent. It is argued that this inequivalence is due to the hyperbolic structure of the "Schr\"odinger-like" equation.
Alvarenga Flavio G.
Batista Antonio Brasil
Fabris Julio Cesar
Goncalves S. V. B.
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