Mathematical structure of loop quantum cosmology
TLDR
In this article, 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 been made explicit, thereby providing a firmer mathematical and conceptual foundation to the subject.Abstract:
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.read more
Citations
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Journal ArticleDOI
Background independent quantum gravity: A Status report
TL;DR: Loop quantum gravity as discussed by the authors is a background-independent, non-perturbative approach to the problem of unification of general relativity and quantum physics, based on a quantum theory of geometry.
Journal ArticleDOI
Quantum Nature of the Big Bang: Improved dynamics
TL;DR: In this article, an improved Hamiltonian constraint operator is introduced in loop quantum cosmology for the isotropic model with a massless scalar field and the big bang is replaced by a quantum bounce.
Journal ArticleDOI
Loop Quantum Cosmology: A Status Report
Abhay Ashtekar,Parampreet Singh +1 more
TL;DR: Loop quantum cosmology (LQC) as mentioned in this paper is the result of applying principles of loop quantum gravity to cosmological settings, where quantum geometry creates a brand new repulsive force which is totally negligible at low spacetime curvature but rises very rapidly in the Planck regime, overwhelming the classical gravitational attraction.
Journal ArticleDOI
Quantum Nature of the Big Bang
TL;DR: The known results on the resolution of the big-bang singularity in loop quantum cosmology are significantly extended, and unlike in other approaches the quantum evolution is deterministic across the deep Planck regime.
Journal ArticleDOI
Loop Quantum Cosmology
TL;DR: In this paper, an application of loop quantum cosmology to homogeneous systems, which removes classical singularities, is presented, where the main effects are introduced into effective classical equations, which allow one to avoid the interpretational problems of quantum theory.
References
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Journal ArticleDOI
Background independent quantum gravity: A Status report
TL;DR: Loop quantum gravity as discussed by the authors is a background-independent, non-perturbative approach to the problem of unification of general relativity and quantum physics, based on a quantum theory of geometry.
Journal ArticleDOI
New variables for classical and quantum gravity.
Abhay Ashtekar,Abhay Ashtekar +1 more
TL;DR: A Hamiltonian formulation of general relativity based on certain spinorial variables is introduced that enables one to imbed the constraint surface in the phase space of Einstein's theory into that of Yang-Mills theory.
Journal ArticleDOI
Discreteness of area and volume in quantum gravity
Carlo Rovelli,Lee Smolin +1 more
TL;DR: In this article, the authors studied the spectrum of the volume in nonperturbative quantum gravity, and showed that the spectrum can be computed by diagonalizing finite dimensional matrices, which can be seen as a generalization of the spin networks.
Journal ArticleDOI
Quantum geometry and black hole entropy
TL;DR: In this article, it was shown that the entropy of a large non-rotating black hole is proportional to its horizon area, and that the constant of proportionality depends upon the Immirzi parameter, which fixes the spectrum of the area operator in loop quantum gravity.