Path integrals and the WKB approximation in loop quantum cosmology

Ashtekar, Abhay; Campiglia, Miguel; Henderson, Adam

doi:10.1103/physrevd.82.124043

Cited by 76 publications

(112 citation statements)

References 33 publications

(85 reference statements)

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“…The effective description of LQC is a delicate and topical issue since it may relate the quantum gravity effects to low-energy physics. The effective equations of LQC are being studied from both the canonical perspective [43][44][45][46] and the path integral perspective [47][48][49][50][51][52][53]. Since the key element in the polymer-like quantization of the previous subsection is to take holonomies rather than connections as basic variables, a heuristic and simple way to get the effective equations is to do the replacementc → sin(μc) µ [30].…”

Section: Effective Equationmentioning

confidence: 99%

Loop Quantum Cosmology, Modified Gravity and Extra Dimensions

Zhang

2016

Universe

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Loop quantum cosmology (LQC) is a framework of quantum cosmology based on the quantization of symmetry reduced models following the quantization techniques of loop quantum gravity (LQG). This paper is devoted to reviewing LQC as well as its various extensions including modified gravity and higher dimensions. For simplicity considerations, we mainly focus on the effective theory, which captures main quantum corrections at the cosmological level. We set up the basic structure of Brans-Dicke (BD) and higher dimensional LQC. The effective dynamical equations of these theories are also obtained, which lay a foundation for the future phenomenological investigations to probe possible quantum gravity effects in cosmology. Some outlooks and future extensions are also discussed.

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Section: Effective Equationmentioning

confidence: 99%

Loop Quantum Cosmology, Modified Gravity and Extra Dimensions

Zhang

2016

Universe

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“…The effective description of LQC is a delicate and topical issue since it may relate the quantum gravity effects to low-energy physics. The effective equations of LQC are being studied from both canonical perspective [44][45][46][47] and path integral perspective [48][49][50][51][52]. Since the key element in the polymer-like quantization of previous subsection is to take holonomies rather than connections as basic variables, a heuristic and simple way to get the effective equations is to do the replacementc → sin(μc) …”

Section: B Effective Equationmentioning

confidence: 99%

Loop quantum modified gravity and its cosmological application

Zhang

2013

Front. Phys.

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A general nonperturvative loop quantization procedure for metric modified gravity is reviewed. As an example, this procedure is applied to scalar-tensor theories of gravity. The quantum kinematical framework of these theories is rigorously constructed. Both the Hamiltonian and master constraint operators are well defined and proposed to represent quantum dynamics of scalar-tensor theories. As an application to models, we set up the basic structure of loop quantum Brans-Dicke cosmology. The effective dynamical equations of loop quantum Brans-Dicke cosmology are also obtained, which lay a foundation for the phenomenological investigation to possible quantum gravity effects in cosmology.

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“…To make a detailed connection with other formulations we use the Feynman phase space path integral procedures considered in [32]. The general idea of the group averaging procedure (see e.g.…”

Section: Quantum Cosmology For the Anisotropic Bianchi I Modelmentioning

confidence: 99%

“…We shall follow here the path integral approach, based on [42] and developed for a timeless framework in [32], which consists essentially in replacing the transition function in Feynman's formalism by the Kernel A(x f , φ f ; x I , φ I ), where the subscripts f and I denote the final and initial states of the system, and regarding the constraint operator exp(iαĈ) in (IV.53) in a purely mathematical sense as a Hamiltonian with evolution time equal to one. That is, e iαĈ = e itĤ whereĤ = αĈ and t = 1.…”

Section: Quantum Cosmology For the Anisotropic Bianchi I Modelmentioning

confidence: 99%

TwistedC⋆-algebra formulation of quantum cosmology with application to the Bianchi I model

et al. 2014

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A twisted C ⋆ -algebra of the extended (noncommutative) Heisenberg-Weyl group has been constructed which takes into account the Uncertainty Principle for coordinates in the Planck length regime. This general construction is then used to generate an appropriate Hilbert space and observables for the noncommutative theory which, when applied to the Bianchi I Cosmology, leads to a new set of equations that describe the quantum evolution of the universe. We find that this formulation matches theories based on a reticular Heisenberg-Weyl algebra in the bouncing and expanding regions of a collapsing Bianchi universe. There is, however, an additional effect introduced by the dynamics generated by the noncommutativity. This is an oscillation in the spectrum of the volume operator of the universe, within the bouncing region of the commutative theories. We show that this effect is generic and produced by the noncommutative momentum exchange between the degrees of freedom in the cosmology. We give asymptotic and numerical solutions which show the above mentioned effects of the noncommutativity.

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Path integrals and the WKB approximation in loop quantum cosmology

Cited by 76 publications

References 33 publications

Loop Quantum Cosmology, Modified Gravity and Extra Dimensions

Loop Quantum Cosmology, Modified Gravity and Extra Dimensions

Loop quantum modified gravity and its cosmological application

TwistedC⋆-algebra formulation of quantum cosmology with application to the Bianchi I model

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