On the Hamiltonian Constraint of Loop Quantum Cosmology

Abstract

In this paper we construct the Hamiltonian constraint operator of loop quantum cosmology using holonomies defined for arbitrary irreducible SU(2) representations labeled by spin J. We show that modifications to the effective semi-classical equations of motion arise both in the gravitational part of the constraint as well as matter terms. The modifications are important for phenomenological investigations of the cosmological imprints of loop quantum cosmology. We discuss the implications for the early universe evolution.

References in corpus (7)

• Black hole entropy in Loop Quantum Gravity
• Black hole entropy from Quantum Geometry
• Oscillatory Universes in Loop Quantum Cosmology and Initial Conditions for Inflation
• Loop Quantum Gravity and the Cyclic Universe
• On the Physical Hilbert Space of Loop Quantum Cosmology
• Effective Hamiltonian for Isotropic Loop Quantum Cosmology
• Coordinate time dependence in Quantum Gravity

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