Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-10-13
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
17 pages, 6 figures, Acepted in IJTP
Scientific paper
Using the ADM formalism in the minisuperspace, we obtain the commutative and noncommutative exact classical solutions and exact wave function to the Wheeler-DeWitt equation with an arbitrary factor ordering, for the anisotropic Bianchi type I cosmological model, coupled to a scalar field, cosmological term and barotropic perfect fluid. We introduce noncommutative scale factors, considering that all minisuperspace variables $\rm q^i$ do not commute, so the symplectic structure was modified. In the classical regime, it is shown that the anisotropic parameter $\rm \beta_{\pm nc}$ and the field $\phi$, for some value in the $\lambda_{eff}$ cosmological term and noncommutative $\theta$ parameter, present a dynamical isotropization up to a critical cosmic time $t_{c}$; after this time, the effects of isotropization in the noncommutative minisuperspace seems to disappear. In the quantum regimen, the probability density presents a new structure that corresponds to the value of the noncommutativity parameter.
Aguero Maximo
Ortiz Camilo
Pimentel Luis O.
Socorro José
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