Loop quantum cosmology in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>dimension

Zhang, Xiangdong

doi:10.1103/physrevd.90.124018

Cited by 14 publications

(42 citation statements)

References 41 publications

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“…Thus as in [19] we just fix = 0. Moreover, note that because the state |0 has zero norm, it is excluded out of the physical Hilbert space.…”

Section: Singularity Resolutionmentioning

confidence: 99%

“…Although LQC is a fruitful theory, nowadays all the discussions are still limited to 4 spacetime dimensions. Recently, LQC has been generalized to the 2 + 1 dimensional case [19]. Hence it is naturally to ask if it is possible to generalize the structure of LQC to the higher spacetime dimensions.…”

Section: Introductionmentioning

confidence: 99%

“…Thus the purpose of the present paper is to investigate the issue of the n + 1 dimensional LQC in this generalized LQG framework. Note that the 2+1 dimensional case is already studied in [19]. Therefore this paper will be devoted to the LQC with n ≥ 3.…”

Section: Introductionmentioning

confidence: 99%

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Higher dimensional loop quantum cosmology

Zhang

2016

Eur. Phys. J. C

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Loop quantum cosmology (LQC) is the symmetric sector of loop quantum gravity. In this paper, we generalize the structure of loop quantum cosmology to the theories with arbitrary spacetime dimensions. The isotropic and homogeneous cosmological model in n + 1 dimensions is quantized by the loop quantization method. Interestingly, we find that the underlying quantum theories are divided into two qualitatively different sectors according to spacetime dimensions. The effective Hamiltonian and modified dynamical equations of n +1 dimensional LQC are obtained. Moreover, our results indicate that the classical big bang singularity is resolved in arbitrary spacetime dimensions by a quantum bounce. We also briefly discuss the similarities and differences between the n + 1 dimensional model and the 3 + 1 dimensional one. Our model serves as a first example of higher dimensional loop quantum cosmology and offers the possibility to investigate quantum gravity effects in higher dimensional cosmology.

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“…Thus as in [19] we just fix = 0. Moreover, note that because the state |0 has zero norm, it is excluded out of the physical Hilbert space.…”

Section: Singularity Resolutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Higher dimensional loop quantum cosmology

Zhang

2016

Eur. Phys. J. C

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“…Establishing the shape of the spectrum F s (T n ) from experimental data and answering the above questions are complicated by the limited number of measurements and their significant errors. In the time of experimental investigation since 1954 [4] the energy characteristics of cg-neutrons generated by muons with various energies E µ in various materials have been measured in six experiments [5], [6], [7], [8], [9], [10]. The spectrum of isolated neutrons F is (T n ) at energies below 90 MeV was obtained in [5], [6].…”

Section: The Generation Of Cosmogenic Neutronsmentioning

confidence: 99%

On the energy spectrum of cosmogenic neutrons

Malgin

2017

J. Exp. Theor. Phys.

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The processes of the generation of cosmogenic neutrons (cg-neutrons) underground are considered. The neutrons produced by cosmic-ray muons in their interactions with matter are called cosmogenic. Deepinelastic πA-collisions of pions in muon-induced hadronic showers are mainly their source at energies above 30 MeV. The characteristics of the energy spectrum for the generation of cg-neutrons have been determined by invoking the additive quark model of deep-inelastic soft processes and the mechanism for the interactions of high-energy nucleons in a nucleus. The three-component shape of the spectrum is explained, and the energy of the "knee" in the spectrum has been found to depend on the mass number A. The peculiarities of deepinelastic πA-scattering lead to the conclusion that the spectrum of cg-neutrons steepens sharply at energies above 1 GeV. The calculated quantitative characteristics of the spectrum are compared with those obtained in measurements.

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“…This operator is anomaly-free in some sense [4,16]. The technique to quantize the Hamiltonian constraint in LQG has also been applied to the coupling of gravity with matter [17], high-dimensional GR [49], the scalar-tensor theories of gravity [50,51], and the symmetry-reduced models of LQG [25,[52][53][54][55]. Moreover, to understand the relation between the canonical and covariant quantum dynamics, one also needs to calculate the matrix elements of the Hamiltonian constraint on given quantum states.…”

Section: The Hamiltonian Constraint Operatormentioning

confidence: 99%

Graphical calculus of volume, inverse volume and Hamiltonian operators in loop quantum gravity

Yang

2017

Eur. Phys. J. C

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To adopt a practical method to calculate the action of geometrical operators on quantum states is a crucial task in loop quantum gravity. In this paper, the graphical calculus based on the original Brink graphical method is applied to loop quantum gravity along the line of previous work. The graphical method provides a very powerful technique for simplifying complicated calculations. The closed formula of the volume operator and the actions of the Euclidean Hamiltonian constraint operator and the so-called inverse volume operator on spin-network states with trivalent vertices are derived via the graphical method. By employing suitable and non-ambiguous graphs to represent the action of operators as well as the spin-network states, we use the simple rules of transforming graphs to obtain the resulting formula. Comparing with the complicated algebraic derivation in some literature, our procedure is more concise, intuitive and visual. The resulting matrix elements of the volume operator is compact and uniform, fitting for both gauge-invariant and gauge-variant spin-network states. Our results indicate some corrections to the existing results for the Hamiltonian operator and inverse volume operator in the literature.

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Loop quantum cosmology in2+1dimension

Cited by 14 publications

References 41 publications

Higher dimensional loop quantum cosmology

Higher dimensional loop quantum cosmology

On the energy spectrum of cosmogenic neutrons

Graphical calculus of volume, inverse volume and Hamiltonian operators in loop quantum gravity

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