Small Cosmological Constant from De Broglie-Bohm Quantum Theor
Jung-Jeng Huang

Jung-Jeng Huang, Department of Mechanical Engineering, Physics Division, Ming Chi University of Technology,
Manuscript received on December 11, 2013. | Revised Manuscript received on December 15, 2013. | Manuscript published on December 25, 2013. | PP: 51-58 | Volume-2 Issue-2, December 2013. | Retrieval Number: B0619122213/2013©BEIESP

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Abstract: We propose a unified mechanism for generating a small cosmological constant through cascade transition in the history of the Universe in the context of de Broglie-Bohm quantum theory. In our previous work we studied the possible effects of trans-Planckian physics on the Bohm quantum trajectories of massless minimally coupled scalar field in de Sitter space. The result showed that for the Corley-Jacobson type dispersion relation with sextic correction, there exists a transition in the evolution of the quantum trajectory from well before horizon exit to well after horizon exit, providing a possible mechanism for generating a small cosmological constant. In this paper we obtain similar transitional behaviour for the Corley-Jacobson type dispersion relation with quartic correction. We find that if we compare the trans-Planckian effects on the Bohm quantum trajectories due to quartic and sextic corrections, the latter is much smaller than the former. We calculate explicitly the finite vacuum energy density due to fluctuations of the inflaton field and show how the cosmological constant reduces during the slow-roll inflation at the grand unification phase transition. Similar reduction mechanisms at the electroweak, quark-hadron and current accelerating phase transitions are also suggested to yield the current small value of the cosmological constant.
Keywords: Cosmological constant, de Broglie-Bohm theoty, Schrödinger picture, trans-Planckian physics.