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Shortcomings of the Big Bounce derivation in Loop Quantum Cosmology · Around

2010

Shortcomings of the Big Bounce derivation in Loop Quantum Cosmology

Cianfrani, Francesco, Montani, Giovanni

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We give a prescription to define in Loop Quantum Gravity the electric field operator related to the scale factor of an homogeneous and isotropic cosmological space-time.

This procedure allows to link the fundamental theory with its cosmological implementation.
In view of the conjugate relation existing between holonomies and fluxes, the edge length and the area of surfaces in the fiducial metric satisfy a duality condition.
As a consequence, the area operator has a discrete spectrum also in Loop Quantum Cosmology.

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C. Rovelli, “Quantum gravity”, Cambridge University Press, Cambridge, (2004), XXIII; T. Thiemann, “Modern Canonical Quantum General Relativity”, (Cambridge University Press, Cambridge, England, 2006); F. Cianfrani, O.M. Lecian, G. Montani, “Fundamentals and recent developments in non-perturbative canonical Quantum Gravity”, arXiv:0805.2503
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2006
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C. Rovelli, “A new look at loop quantum gravity”, arXiv:1004.1780

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