Mathematical structure of loop quantum cosmology

By Abhay Ashtekar, M. Bojowald, J. Lewandowski. 2003

768 citations recorded by the source corpus.

Applications of Riemannian quantum geometry to cosmology have had notable successes. In particular, the fundamental discreteness underlying quantum geometry has led to a natural resolution of the big bang singularity. However, the precise mathematical structure underlying loop quantum cosmology and the sense in which it implements the full quantization program in a symmetry reduced model has not been made explicit. The purpose of this paper is to address these issues, thereby providing a firmer mathematical and conceptual foundation to the subject.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f0941ca653156a9e8848a6221d3a8ab927676db8

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Citations in the corpus

Loop quantization of the Schwarzschild interior revisited (2015, methodology): “black hole interior [6], the strategy followed a particular quantization of isotropic FLRW models [11, 12].”
Minimal Length Scale Scenarios for Quantum Gravity (2012, background): “(For this, one does not have to use the sinus function in particular; any almost-periodic function would do [40], but the sinus is the easiest to deal with.”
Extension of the quantum theory of cosmological perturbations to the Planck era (2012, background): “In the first step, a specific kinetic framework [59] can be selected by a uniqueness theorem [60] along the lines of those in full LQG [61, 62].”
Quantum nature of the big bang: An analytical and numerical investigation (2006, methodology): “In this paper, we will discuss the one that has been used in the literature [12, 14, 20].”
From black holes to white holes: a quantum gravitational, symmetric bounce (2017, neutral): “Preservation of this condition upon evolution 0 ≈ ˙̃Ψ = {P1, HLQC} − 1, (B1) 21 and after evaluation on shell, allows us to fix the lapse function N = c b γ2 8π √ δc 2 |O2| cosh (4GγP2) 1 δb √ 1− b2o tanh2 [ GγboT̃ ] .”
Loop quantum cosmology of Bianchi type IX models (2009, neutral): “[7] A.”
Loop quantum cosmology of Bianchi I models (2009, methodology): “) To evaluate the symplectic structure of the symmetry reduced theory, as in the isotropic case [7], we begin with the expression of the symplectic structure in the full theory and simply restrict the integration to the cell V.”
Spherically symmetric quantum geometry: Hamiltonian constraint (2005, positive): “Homogeneous connection components transform as scalars and thus are implemented via ‘point holonomies’ [4, 7, 47, 48] such as exp iγKφ(v) rather than holonomies along edges.”
The pre-inflationary dynamics of loop quantum cosmology: confronting quantum gravity with observations (2012, background): “[21] A.”
Loop quantum cosmology: a status report (2011, methodology): “Roughly, at a key step in the procedure, the Hamiltonian constraint operator of [45] implicitly used a kinematic 3-metric q̊ab defined by the co-moving coordinates rather than the physical metric qab = a (2)q̊ab (where a is the scale factor).”
Quantum geometry and the Schwarzschild singularity (2005, methodology): “As discussed in [9], considerations from the full theory imply that μo should not be regarded as a regulator; rather, the μo-dependence of this operator should be regarded as a quantization ambiguity.”
Introduction to Loop Quantum Cosmology (2011, methodology): “After the early papers by Bojowald, the kinematic structure of LQC was revised and more rigorously established [9], which made it possible to complete the quantization of the model in presence of a homogeneous massless scalar field minimally coupled to the geometry, as well as to study the resulting”
Quantum extension of the Kruskal spacetime (2018, positive): “The kinematical framework introduced in [1, 19] and the idea of incorporating quantum gravity corrections to dynamics by representing curvature in terms of holonomies around ‘elementary plaquettes’ continue to be widely used in the analysis of cosmological and black hole singularities.”
Quantum-Spacetime Phenomenology (2008, background): “[125, 94, 126, 92] and references therein, but one must inevitably resort to rather drastic approximations, since a full LQG analysis is not possible at present.”
Towards spinfoam cosmology (2010, background): “[39] Abhay Ashtekar, Martin Bojowald, and Jerzy Lewandowski.”
Quantum Nature of the Big Bang: Improved dynamics (2006, methodology): “To summarize, the Hamiltonian constraint will be improved by implementing the physical idea of [4] in a more satisfactory manner.”