Isotropic Loop Quantum Cosmology with Matter II: The Lorentzian Constraint

Details Isotropic Loop Quantum Cosmology with Matter II: The Lorentzian Constraint Isotropic Loop Quantum Cosmology with Matter II: The Lorentzian Constraint

2003-09-05

arxiv.org/abs/gr-qc/0309035v1

Phys.Rev. D68 (2003) 124023

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

19 pages, 4 figures

Scientific paper

10.1103/PhysRevD.68.124023

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.

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