Reparameterization invariants for anisotropic Bianchi I cosmology with a massless scalar source

Salisbury, Donald; Helpert, J.; Schmitz, Albert T.

doi:10.1007/s10714-007-0541-0

Cited by 12 publications

(16 citation statements)

References 37 publications

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“…My aim is technically much simpler, namely, to find a theory that has enough GR-like behavior to threaten to lose time evolution just as GR doestime reparametrization invariance with a Hamiltonian constraint quadratic in the momenta-but simple enough that explicitly finding time evolution is easy when one looks in the right place. Confusingly, the counting of degrees of freedom in Bianchi cosmologies depends on the intended interpretation and also the global topology (Pons and Shepley, 1998;Ashtekar and Samuel, 1991;Salisbury et al, 2008). If one views such cosmologies as a sector of General Relativity (without preferred simultaneity), then solutions related by a 4-dimensional coordinate transformation will count as equivalent.…”

Section: Illustration Via Homogeneous Truncation Of Grmentioning

confidence: 99%

“…There will be no occasion to worry about homogeneity-preserving diffeomorphisms or the number of degrees of freedom. Leaving redundant components in the spatial metric is useful in order to preserve the visual-mathematical resemblance between a tensor (matrix) field in GR and a matrix, as opposed to whittling it down to its diagonal elements (c.f., (Goldberg and Klotz, 1973;Ryan and Shepley, 1975;Salisbury et al, 2008)). My treatment also assumes the simplest version of homogeneity, namely, with the three spatial Killing vector fields all commuting (vanishing structure constants, Bianchi type I), so one can simply keep x 0 = t and drop x i (i = 1, 2, 3).…”

Section: Illustration Via Homogeneous Truncation Of Grmentioning

confidence: 99%

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Change in Hamiltonian general relativity from the lack of a time-like Killing vector field

Pitts

2014

Studies in History and Philosophy of Science Part B: Studies in

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In General Relativity in Hamiltonian form, change has seemed to be missing, defined only asymptotically, or otherwise obscured at best, because the Hamiltonian is a sum of first-class constraints and a boundary term and thus supposedly generates gauge transformations. Attention to the gauge generator G of Rosenfeld, Anderson, Bergmann, Castellani et al., a specially tuned sum of first-class constraints, facilitates seeing that a solitary first-class constraint in fact generates not a gauge transformation, but a bad physical change in electromagnetism (changing the electric field) or General Relativity. The change spoils the Lagrangian constraints, Gauss's law or the Gauss-Codazzi relations describing embedding of space into space-time, in terms of the physically relevant velocities rather than auxiliary canonical momenta. While Maudlin and Healey have defended change in GR much as G. E. Moore resisted skepticism, there remains a need to exhibit the technical flaws in the no-change argument.Insistence on Hamiltonian-Lagrangian equivalence, a theme emphasized by Mukunda, Castellani, Sugano, Pons, Salisbury, Shepley and Sundermeyer among others, holds the key. Taking objective change to be ineliminable time dependence, one recalls that there is change in vacuum GR just in case there is no time-like vector field ξ α satisfying Killing's equation £ ξ gµν = 0, because then there exists no coordinate system such that everything is independent of time. Throwing away the spatial dependence of GR for convenience, one finds explicitly that the time evolution from Hamilton's equations is real change just when there is no time-like Killing vector. The inclusion of a massive scalar field is simple. No obstruction is expected in including spatial dependence and coupling more general matter fields. Hence change is real and local even in the Hamiltonian formalism.The considerations here resolve the Earman-Maudlin standoff over change in Hamiltonian General Relativity: the Hamiltonian formalism is helpful, and, suitably reformed, it does not have absurd consequences for change. Hence the classical problem of time is resolved, apart from the issue of observables, for which the solution is outlined. The Lagrangian-equivalent Hamiltonian analysis of change in General Relativity is compared to Belot and Earman's treatment. The more serious quantum problem of time, however, is not automatically resolved due to issues of quantum constraint imposition.

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Section: Illustration Via Homogeneous Truncation Of Grmentioning

confidence: 99%

Section: Illustration Via Homogeneous Truncation Of Grmentioning

confidence: 99%

Change in Hamiltonian general relativity from the lack of a time-like Killing vector field

Pitts

2014

Studies in History and Philosophy of Science Part B: Studies in

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“…In order to grasp the precise physical meanings of the Ashtekar variables, which are the fundamental degrees of freedom in LQC, the formulations in metric variables (also see [11]) and in Ashtekar variables are both investigated.…”

Section: Classical Dynamicsmentioning

confidence: 99%

Effective dynamics, big bounces, and scaling symmetry in Bianchi type I loop quantum cosmology

Chiou

2007

Phys. Rev. D

134

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The detailed formulation for loop quantum cosmology (LQC) in the Bianchi I model with a scalar massless field has been constructed. In this paper, its effective dynamics is studied in two improved strategies for implementing the LQC discreteness corrections. Both schemes show that the big bang is replaced by the big bounces, which take place up to three times, once in each diagonal direction, when the area or volume scale factor approaches the critical values in the Planck regime measured by the reference of the scalar field momentum. These two strategies give different evolutions: In one scheme, the effective dynamics is independent of the choice of the finite sized cell prescribed to make Hamiltonian finite; in the other, the effective dynamics reacts to the macroscopic scales introduced by the boundary conditions. Both schemes reveal interesting symmetries of scaling, which are reminiscent of the relational interpretation of quantum mechanics and also suggest that the fundamental spatial scale (area gap) may give rise to a temporal scale.

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“…The details of time identification procedure in terms of various dynamical variables of the theory before quantization is done has been investigated in [17] where a Robertson-Walker universe filled with a scalar field is quantized. Also in [18] a choice of time in terms of a massless scalar field is discussed in a Bianchi-I classical cosmology based on the method developed in [19].…”

Section: Introductionmentioning

confidence: 99%

“…In the case of a scalar field as the source of gravity, the scalar field itself can play the role of time as is the case in [17] and [18]. Another matter field which has occasionally been studied in the literatures is the massless or massive spinor field as the source of gravity.…”

Section: Introductionmentioning

confidence: 99%

Time reparameterization in Bianchi type I spinor cosmology

Vakili

Sepangi

2008

Annals of Physics

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The problem of time reparameterization is addressed at both the classical and quantum levels in a Bianchi-I universe in which the matter source is a massive Dirac spinor field. We take the scale factors of the metric as the intrinsic time and their conjugate momenta as the extrinsic time. A scalar character of the spinor field is identified as a representation of the extrinsic time. The construction of the field equations and quantization of the model is achieved by solving the Hamiltonian constraint after time identification has been dealt with. This procedure leads to a true Hamiltonian whose exact solutions for the above choices of time are presented.

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Reparameterization invariants for anisotropic Bianchi I cosmology with a massless scalar source

Abstract: Intrinsic time-dependent invariants are constructed for classical, flat, homogeneous, anisotropic cosmology with a massless scalar material source. Invariance under the time reparameterizationinduced canonical symmetry group is displayed explicitly.

Cited by 12 publications

References 37 publications

Change in Hamiltonian general relativity from the lack of a time-like Killing vector field

Change in Hamiltonian general relativity from the lack of a time-like Killing vector field

Effective dynamics, big bounces, and scaling symmetry in Bianchi type I loop quantum cosmology

Time reparameterization in Bianchi type I spinor cosmology

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