Isotropic Loop Quantum Cosmology with Matter II: The Lorentzian Constraint

Abstract

The Lorentzian Hamiltonian constraint is solved for isotropic loop quantum cosmology coupled to a massless scalar field. As in the Euclidean case, the discreteness of quantum geometry removes the classical singularity from the quantum Friedmann models. In spite of the absence of the classical singularity, a modified DeWitt initial condition is incompatible with a late-time smooth behavior. Further, the smooth behavior is recovered only for positive or negatives times but not both. An important feature, which is shared with the Euclidean case, is a minimal initial energy of the order of the Planck energy required for the system to evolve dynamically. By forming wave packets of the matter field an explicit evolution in terms of an internal time is obtained.

19 pages, 4 figures

References in corpus (11)

• Absence of Singularity in Loop Quantum Cosmology
• Isotropic Loop Quantum Cosmology
• Inflation from Quantum Geometry
• The Inverse Scale Factor in Isotropic Quantum Geometry
• Homogeneous Loop Quantum Cosmology
• Quantization Ambiguities in Isotropic Quantum Geometry
• Dynamical Initial Conditions in Quantum Cosmology
• The Semiclassical Limit of Loop Quantum Cosmology
• Operators for quantized directions
• Isotropic Loop Quantum Cosmology with Matter
• Gravitational Statistical Mechanics: A model

Cited by in corpus (9)

• Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
• Loop Quantum Cosmology
• Spherically Symmetric Quantum Geometry: Hamiltonian Constraint
• Big Crunch Avoidance in k = 1 Semi-Classical Loop Quantum Cosmology
• Effective equations for isotropic quantum cosmology including matter
• Difficulties with Recollapsing models in Closed Isotropic Loop Quantum Cosmology
• Coordinate time dependence in Quantum Gravity
• Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
• Loop quantum cosmology and the Wheeler-De Witt equation