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Advances in High Energy Physics
Volume 2012 (2012), Article ID 312841, 19 pages
http://dx.doi.org/10.1155/2012/312841
Research Article

Bohm Quantum Trajectories of Scalar Field in Trans-Planckian Physics

Physics Division, Department of Mechanical Engineering, Ming Chi University of Technology, Taishan, New Taipei City 24301, Taiwan

Received 17 October 2011; Revised 7 December 2011; Accepted 29 December 2011

Academic Editor: Kadayam S. Viswanathan

Copyright © 2012 Jung-Jeng Huang. 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.

Abstract

In lattice Schrödinger picture, we investigate the possible effects of trans-Planckian physics on the quantum trajectories of scalar field in de Sitter space within the framework of the pilot-wave theory of de Broglie and Bohm. For the massless minimally coupled scalar field and the Corley-Jacobson type dispersion relation with sextic correction to the standard-squared linear relation, we obtain the time evolution of vacuum state of the scalar field during slow-roll inflation. We find that there exists a transition in the evolution of the quantum trajectory from well before horizon exit to well after horizon exit, which provides a possible mechanism to solve the riddle of the smallness of the cosmological constant.