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arXiv · 0910.2449

Scalar field in the Bianchi I: Non commutative classical and Quantum Cosmology

J. Socorro·Luis O. Pimentel·C. Ortiz·M. Aguero
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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 $\rm β_{\pm nc}$ and the field $ϕ$, for some value in the $λ_{eff}$ cosmological term and noncommutative $θ$ 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.

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J. Socorro, Luis O. Pimentel, C. Ortiz, M. Aguero. 2009-10-13. Scalar field in the Bianchi I: Non commutative classical and Quantum Cosmology. https://doi.org/10.1007/s10773-009-0164-1

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