Generalized uncertainty principle in Bianchi type I quantum cosmology
Abstract
We study a quantum Bianchi type I model in which the dynamical variables of the corresponding minisuperspace obey the generalized Heisenberg algebra. Such a generalized uncertainty principle has its origin in the existence of a minimal length suggested by quantum gravity and sting theory. We present approximate analytical solutions to the corresponding Wheeler DeWitt equation in the limit where the scale factor of the universe is small and compare the results with the standard commutative and noncommutative quantum cosmology. Similarities and differences of these solutions are also discussed.
 Publication:

Physics Letters B
 Pub Date:
 July 2007
 DOI:
 10.1016/j.physletb.2007.06.015
 arXiv:
 arXiv:0706.0273
 Bibcode:
 2007PhLB..651...79V
 Keywords:

 04.60.m;
 04.60.Ds;
 04.60.Kz;
 Quantum gravity;
 Canonical quantization;
 Lower dimensional models;
 minisuperspace models;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 8 pages, 3 figures, to appear in PLB