Algorithmic approach to cosmological coherent state expectation values in loop quantum gravity

Liegener, Klaus; Rudnicki, Łukasz

doi:10.1088/1361-6382/ac226f

Cited by 14 publications

(28 citation statements)

References 62 publications

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“…The result of H E in[31] is the same as ours (see (6.1)) up to an overall constant and (η, ξ) → (−η, −ξ).…”

supporting

confidence: 81%

“…Recent research works have been focus on building models of LQG on a single graph γ [17,[25][26][27][28][29][30][31]. In particular, the quantum dynamics of the reduced phase space LQG is formulated on the cubic lattice γ as a path integral [7,18]…”

Section: Introductionmentioning

confidence: 99%

“…Note added in proof: During finalizing this paper, we became aware that the O( ) correction of the Euclidean part H E in H [1] was derived independently in [31] 1 .…”

Section: Introductionmentioning

confidence: 99%

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First-Order Quantum Correction in Coherent State Expectation Value of Loop-Quantum-Gravity Hamiltonian: Overview and Results

Zhang¹,

Song²,

Han³

2020

Preprint

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Given the Loop-Quantum-Gravity (LQG) non-graph-changing Hamiltonian H[N ], the coherent state expectation value H[N ] admits an semiclassical expansion in 2 p . In this paper, we compute explicitly the expansion of H[N ] on the cubic graph to the linear order in 2 p , when the coherent state is peaked at the homogeneous and isotropic data of cosmology. In our computation, a powerful algorithm is developed to overcome the complexity in computing H[N ] . In particular, some key innovations in our algorithm substantially reduce the computational complexity in the Lorentzian part of H[N ] . In addition, some effects in cosmology from the quantum correction in H[N ] are discussed at the end of this paper.

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“…The result of H E in[31] is the same as ours (see (6.1)) up to an overall constant and (η, ξ) → (−η, −ξ).…”

supporting

confidence: 81%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

First-Order Quantum Correction in Coherent State Expectation Value of Loop-Quantum-Gravity Hamiltonian: Overview and Results

Zhang¹,

Song²,

Han³

2020

Preprint

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show abstract

“…On the other hand, the left hand side -that is, the double commutator between operators in the full theory -can be computed explicitly (see [53] for details). The evaluation gives…”

Section: No-go Statementsmentioning

confidence: 99%

Challenges in recovering a consistent cosmology from the effective dynamics of loop quantum gravity

2019

Self Cite

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We reexamine a set of existing procedures aimed at recovering the effective description of the dynamics of LQG in the context of cosmological solutions. In particular, the studies of those methods, to which the choice of cuboidal graphs and graph-preserving Hamiltonian is central, result in the formulation of a set of no-go statements, severely limiting the possibility of recovering a physically consistent effective dynamics this way.1 In LQG, the space of states consists of cylindrical functions supported on graphs. A graph-preserving operator is an operator which preserves the subspace of cylindrical functions supported on each given graph [17]. 2 The most popular convention is: v = 2πG γ √ ∆p 3/2 and b = c ∆/p, where ∆ is the so-called "area-gap" [15].

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“…The idea put forward in [10,11] was to restrict the action of the scalar constraint to a discrete lattice and semiclassical geometries approximated by said lattice. Using gauge coherent states from [12][13][14][15][16] for the SU(2)-version of the Ashtekar-Barbero variables, this task has been explicitly carried out in [17][18][19]. In particular, the expectation value of the scalar constraint proposed in [8] was computed for semiclassical states approximating spatially-flat, isotropic Friedmann-Lemaître-Robertson-Walker (FLRW) cosmology with matter sourced by a massless scalar field.…”

Section: Introductionmentioning

confidence: 99%

Some physical implications of regularization ambiguities in SU(2) gauge-invariant loop quantum cosmology

Liegener

Singh

2019

Phys. Rev. D

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The way physics of loop quantum gravity is affected by the underlying quantization ambiguities is an open question. We address this issue in the context of loop quantum cosmology using gauge-covariant fluxes. Consequences are explored for two choices of regularization parameters: µ 0 andμ in presence of a positive cosmological constant, and two choices of regularizations of the Hamiltonian constraint in loop quantum cosmology: the standard and the Thiemann regularization. We show that novel features of singularity resolution and bounce, occurring due to gauge-covariant fluxes, exist also for Thiemann-regularized dynamics. The µ 0 -scheme is found to be unviable as in standard loop quantum cosmology when a positive cosmological constant is included. Our investigation brings out a surprising result that the nature of emergent matter in the pre-bounce regime is determined by the choice of regulator in the Thiemann regularization of the scalar constraint whether or not one uses gauge-covaraint fluxes. Unlikeμ-scheme where the emergent matter is a cosmological constant, the emergent matter in µ 0 -scheme behaves as a string gas.

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Algorithmic approach to cosmological coherent state expectation values in loop quantum gravity

Cited by 14 publications

References 62 publications

First-Order Quantum Correction in Coherent State Expectation Value of Loop-Quantum-Gravity Hamiltonian: Overview and Results

First-Order Quantum Correction in Coherent State Expectation Value of Loop-Quantum-Gravity Hamiltonian: Overview and Results

Challenges in recovering a consistent cosmology from the effective dynamics of loop quantum gravity

Some physical implications of regularization ambiguities in SU(2) gauge-invariant loop quantum cosmology

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