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Scalar field in the Bianchi I: Non commutative classical and Quantum Cosmology
- Publication Year :
- 2009
-
Abstract
- 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.<br />Comment: 17 pages, 6 figures, Acepted in IJTP
- Subjects :
- General Relativity and Quantum Cosmology
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.0910.2449
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s10773-009-0164-1