Positive cosmological constant in loop quantum cosmology
Abstract
The k=0 FriedmannLemaitreRobertsonWalker model with a positive cosmological constant and a massless scalar field is analyzed in detail. If one uses the scalar field as relational time, new features arise already in the Hamiltonian framework of classical general relativity: In a finite interval of relational time, the universe expands out to infinite proper time and zero matter density. In the deparametrized quantum theory, the true Hamiltonian now fails to be essentially selfadjoint both in the WheelerDeWitt approach and in loop quantum cosmology. Irrespective of the choice of the selfadjoint extension, the bigbang singularity persists in the WheelerDeWitt theory while it is resolved and replaced by a big bounce in loop quantum cosmology. Furthermore, the quantum evolution is surprisingly insensitive to the choice of the selfadjoint extension. This may be a special case of a yettobe discovered general property of a certain class of symmetric operators that fail to be essentially selfadjoint.
 Publication:

Physical Review D
 Pub Date:
 March 2012
 DOI:
 10.1103/PhysRevD.85.064001
 arXiv:
 arXiv:1112.0360
 Bibcode:
 2012PhRvD..85f4001P
 Keywords:

 04.60.Kz;
 03.65.Sq;
 04.60.Pp;
 98.80.Qc;
 Lower dimensional models;
 minisuperspace models;
 Semiclassical theories and applications;
 Loop quantum gravity quantum geometry spin foams;
 Quantum cosmology;
 General Relativity and Quantum Cosmology;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 High Energy Physics  Theory
 EPrint:
 36 pages, 6 figures, RevTex4