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

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 ${\mathrm{q}}^{\mathrm{i}}$ do not commute, so the symplectic structure was modified. In the classical regime, it is shown that the anisotropic parameter ${\beta }_{\pm \mathrm{nc}}$ and the field $\varphi$, 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.

17 pages, 6 figures, Acepted in IJTP

References in corpus (8)

• Dilaton Cosmology, Noncommutativity and Generalized Uncertainty Principle
• Bianchi spacetimes in noncommutative phase-space
• Generalized uncertainty principle in Bianchi type I quantum cosmology
• Deformed phase space in a two dimensional minisuperspace model
• A fundamental length as a candidate for dark energy: a DSR inspired FRW spacetime
• (Non)commutative isotropization in Bianchi I with Barotropic perfect fluid and $\Lambda$ Cosmological
• Thermodynamics of noncommutative de Sitter spacetime
• The cosmological implications of a fundamental length: a DSR inspired de-Sitter spacetime

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• Fractional Scalar Field Cosmology
• Classical and quantum bicosmology with noncommutativity
• Exact Kantowski-Sachs spacetimes in Einstein-Aether Scalar field theory
• Accelerating cosmologies in an integrable model with noncommutative minisuperspace variables