The Bianchi IX model in loop quantum cosmology

Bojowald, Martin; Date, Ghanashyam; Hossain, Golam Mortuza

doi:10.1088/0264-9381/21/14/015

Cited by 71 publications

(88 citation statements)

References 42 publications

(99 reference statements)

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“…8. In this scenario, there are only finitely many reflections which does not lead to chaotic behavior but instead results in asymptotic Kasner behavior [114]. Comparing Fig.…”

Section: Applicationsmentioning

confidence: 85%

Homogeneous loop quantum cosmology

Bojowald

2003

Class. Quantum Grav.

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167

364

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Quantum gravity is expected to be necessary in order to understand situations where classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e. the fact that the backward evolution of a classical space-time inevitably comes to an end after a finite amount of proper time. This presents a breakdown of the classical picture and requires an extended theory for a meaningful description. Since small length scales and high curvatures are involved, quantum effects must play a role. Not only the singularity itself but also the surrounding space-time is then modified. One particular realization is loop quantum cosmology, an application of loop quantum gravity to homogeneous systems, which removes classical singularities. Its implications can be studied at different levels. Main effects are introduced into effective classical equations which allow to avoid interpretational problems of quantum theory. They give rise to new kinds of early universe phenomenology with applications to inflation and cyclic models. To resolve classical singularities and to understand the structure of geometry around them, the quantum description is necessary. Classical evolution is then replaced by a difference equation for a wave function which allows to extend space-time beyond classical singularities. One main question is how these homogeneous scenarios are related to full loop quantum gravity, which can be dealt with at the level of distributional symmetric states. Finally, the new structure of space-time arising in loop quantum gravity and its application to cosmology sheds new light on more general issues such as time.

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“…8. In this scenario, there are only finitely many reflections which does not lead to chaotic behavior but instead results in asymptotic Kasner behavior [114]. Comparing Fig.…”

Section: Applicationsmentioning

confidence: 85%

Homogeneous loop quantum cosmology

Bojowald

2003

Class. Quantum Grav.

Self Cite

167

364

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“…(The latter can be viewed as providing a natural cut-off on intrinsic curvature, analogously to the extrinsic curvature cut-off from a quantum matter Hamiltonian in a homogeneous situation.) The non-perturbative modifications have mainly been used so far in the Bianchi IX model where they remove the classical chaos [22,82]. They are derived by quantizing the spin connection potential term of the Hamiltonian constraint in accordance with the general scheme described above.…”

Section: Physical Applicationsmentioning

confidence: 99%

Spherically symmetric quantum geometry: Hamiltonian constraint

Bojowald¹,

Swiderski²

2006

Class. Quantum Grav.

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138

213

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Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and Lorentzian Hamiltonian constraints. The construction fits completely into the general scheme available in loop quantum gravity for the quantization of the full theory as well as symmetric models. This then presents a further consistency check of the whole scheme in inhomogeneous situations, lending further credence to the physical results obtained so far mainly in homogeneous models. New applications in particular of the spherically symmetric model in the context of black hole physics are discussed.

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“…While the topic of the isotropic and homogeneous sector of the LQC originated in [6] is well understood [15,16,17,18,19,20,21] there still is work to be done in the homogeneous, but nonisotropic sector. Although loop quantum dynamics is not fully understood in this sector, already the first calculations in the quantum homogeneous models [7,8] suggest a completely different structure of the space-time near classical singularities. After the discovery of the so-called "improved scheme" in [16], analytical issues of kinematics and dynamics were studied in detail in the case of the simplest homogeneous diagonal Bianchi type I (BI) model [14].…”

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confidence: 99%

Loop quantum cosmology of diagonal Bianchi type I model: Simplifications and scaling problems

Szulc

2008

Phys. Rev. D

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A simplified theory of the diagonal Bianchi type I model coupled with a massless scalar field in loop quantum cosmology is constructed according to theμ scheme. Kinematical and physical sectors of the theory are under good analytical control as well as the scalar constraint operator. Although it is possible to compute numerically the nonsingular evolution of the three gravitational degrees of freedom, the naive implementation of theμ scheme to the diagonal Bianchi type I model is problematic. The lack of the full invariance of the theory with respect to the fiducial cell and fiducial metric scaling causes serious problems in the semiclassical limit of the theory. Because of this behavior it is very difficult to extract reasonable physics from the model. The weaknesses of the implementation of theμ scheme to the Bianchi I model do not imply limitations of theμ scheme in the isotropic case.

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The Bianchi IX model in loop quantum cosmology

Cited by 71 publications

References 42 publications

Homogeneous loop quantum cosmology

Homogeneous loop quantum cosmology

Spherically symmetric quantum geometry: Hamiltonian constraint

Loop quantum cosmology of diagonal Bianchi type I model: Simplifications and scaling problems

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