Quantum geometrodynamics of the Bianchi IX cosmological model

A way of constructing mathematically correct quantum geometrodynamics of a closed universe is presented. The resulting theory appears to be gauge-noninvariant and thus consistent with the observation conditions of a closed universe, by that being considerably distinguished from the traditional Wheeler–DeWitt one. For the Bianchi-IX cosmological model it is shown that a normalizable wave function of the universe depends on time, allows the standard probability interpretation and satisfies a gauge-noninvariant dynamical Schrödinger equation. The Wheeler–DeWitt quantum geometrodynamics is represented a singular, BRST-invariant solution to the Schrödinger equation having no property of normalizability.

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Some examples for different descriptions of energy–momentum density in the context of Bianchi IX cosmological model

Indian Journal of Physics ◽

10.1007/s12648-012-0131-1 ◽

2012 ◽

Vol 86 (10) ◽

pp. 919-923 ◽

Cited By ~ 9

Author(s):

Z. Nourinezhad ◽

S. H. Mehdipour

Keyword(s):

Cosmological Model ◽

Momentum Density ◽

Bianchi Ix

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Loop quantum cosmology of Bianchi IX: Inclusion of inverse triad corrections

International Journal of Modern Physics D ◽

10.1142/s0218271816420116 ◽

2016 ◽

Vol 25 (08) ◽

pp. 1642011 ◽

Cited By ~ 7

Author(s):

Alejandro Corichi ◽

Asieh Karami

Keyword(s):

Cosmological Model ◽

Quantum Cosmology ◽

Bianchi Type ◽

Loop Quantum Cosmology ◽

Hamiltonian Constraint ◽

Bianchi Ix ◽

Text Model ◽

Loop Quantization

We consider the loop quantization of the (diagonal) Bianchi type IX cosmological model. We explore different quantization prescriptions that extend the work of Wilson-Ewing and Singh. In particular, we study two different ways of implementing the so-called inverse triad corrections. We construct the corresponding Hamiltonian constraint operators and show that the singularity is formally resolved. We find the effective equations associated with the different quantization prescriptions, and study the relation with the isotropic [Formula: see text] model that, classically, is contained within the Bianchi IX model. Somewhat surprisingly, we find the most natural quantization does not reduce to the [Formula: see text] model. We use geometrically defined scalar observables to explore the physical implications of each of these theories. This is the first part in a series of papers analyzing different aspects of the Bianchi IX model, with inverse corrections, within loop quantum cosmology (LQC).

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