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Advances in High Energy Physics
Volume 2016 (2016), Article ID 6705021, 12 pages
Research Article

Time-Dependent Toroidal Compactification Proposals and the Bianchi Type I Model: Classical and Quantum Solutions

Departamento de Física, DCI, Universidad de Guanajuato, Campus León, Loma del Bosque No. 103 Colonia Lomas del Campestre, Apartado Postal E-143, 37150 León, GTO, Mexico

Received 19 January 2016; Revised 22 April 2016; Accepted 5 May 2016

Academic Editor: Elias C. Vagenas

Copyright © 2016 L. Toledo Sesma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.


We construct an effective four-dimensional model by compactifying a ten-dimensional theory of gravity coupled with a real scalar dilaton field on a time-dependent torus. This approach is applied to anisotropic cosmological Bianchi type I model for which we study the classical coupling of the anisotropic scale factors with the two real scalar moduli produced by the compactification process. Under this approach, we present an isotropization mechanism for the Bianchi I cosmological model through the analysis of the ratio between the anisotropic parameters and the volume of the Universe which in general keeps constant or runs into zero for late times. We also find that the presence of extra dimensions in this model can accelerate the isotropization process depending on the momenta moduli values. Finally, we present some solutions to the corresponding Wheeler-DeWitt (WDW) equation in the context of standard quantum cosmology.