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    188宝金博页面版: [精品]A Decrumpling Model of the Universe

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    内容提示： arXiv:gr-qc/9607049v1 23 Jul 1996July 20, 1996A Decrumpling Model of the UniverseM. Khorrami1,2, R. Mansouri3,4,?, M. Mohazzab5,1Department of Physics, Tehran University, North-Kargar Ave. Tehran, Iran.2Institute for Advanced Studies in Basic Sciences, P.O.Box 159, Gava Zang, Zan-jan 45195, Iran.3Department of Physics, Sharif University of Technology, P.O.Box 9161, Tehran11365, Iran.4Universitaet Potsdam, Mathematisches Institut, Kosmologie Gruppe, Potsdam,Germany.5Physics Department, Brown University, P...

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    arXiv:gr-qc/9607049v1 23 Jul 1996July 20, 1996A Decrumpling Model of the UniverseM. Khorrami1,2, R. Mansouri3,4,∗, M. Mohazzab5,1Department of Physics, Tehran University, North-Kargar Ave. Tehran, Iran.2Institute for Advanced Studies in Basic Sciences, P.O.Box 159, Gava Zang, Zan-jan 45195, Iran.3Department of Physics, Sharif University of Technology, P.O.Box 9161, Tehran11365, Iran.4Universitaet Potsdam, Mathematisches Institut, Kosmologie Gruppe, Potsdam,Germany.5Physics Department, Brown University, Providence RI. 02912, USA.∗E-Mail: rmansouri@aip.deAbstract: Assuming a cellular structure for the space-time, we propose a model in whichthe expansion of the universe is understood as a decrumpling process, much like the onewe know from polymeric surfaces. The dimension of space is then a dynamical real vari-able. The generalized Friedmann equation, derived from a Lagrangian, and the generalizedequation of continuity for the matter content of the universe, give the dynamics of ourmodel universe. This leads to an oscillatory non-singular model with two turning pointsfor the dimension of space.The picture we are proposing for the space-time is a generalization of polymeric ortethered surfaces, which are in turn simple generalizations of linear polymers to two-dimensionally connected networks [1,2]. Visualizing the universe as a piece of paper,then the crumpled paper will stand for the state of the early universe [3]. As we arenot going to develop yet a statistical mechanical model for our decrumpling universe,the dynamical model we are proposing in this paper could as well be interpreted asa generalization of fluid membranes [4]. In this case we can visualize the universeas a clay, which can be formed to a three dimensional ball, to a two dimensionaldisc, or even to a one dimensional string. In each case the effective dimension of theuniverse is a continuous number between the dimension of the embedding space andsome D0which could be 3. To study the crumpling phenomenon in the statisticalphysics one needs to define an embedding space, which does not exist in our case.Therefore, we assume an embedding space of arbitrary high dimension D, which isallowed to be infinite. This is necessary, because the crumpling is highly dependenton the dimension of embedding space.Now, imagine the model universe to be the time evolution of a D-space embedded ina space with arbitrary large, maybe infinite, dimension D. To model the crumpling,we assume the D-space to be consisted of cells with characteristic size of about1

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