Gravitation and Cosmology

, Volume 19, Issue 3, pp 171–177 | Cite as

Quantum billiards in multidimensional models with fields of forms

  • V. D. IvashchukEmail author
  • V. N. Melnikov


A Bianchi type I cosmological model in (n + 1)-dimensional gravity with several forms is considered. When the electric non-composite brane ansatz is adopted, the Wheeler-DeWitt (WDW) equation for the model, written in a conformally covariant form, is analyzed. Under certain restrictions, asymptotic solutions to the WDW equation near the singularity are found, which reduce the problem to the so-called quantum billiard on the (n − 1)-dimensional Lobachevsky space ℍ n−1. Two examples of quantum billiards are considered: a 2-dimensional quantum billiard for a 4D model with three 2-forms and a 9D quantum billiard for an 11D model with 120 4-forms, whichmimics the SM2-brane sector of D = 11 supergravity. For certain solutions, vanishing of the wave function at the singularity is proved.


Cosmological Model Asymptotic Solution Bianchi Type Multidimensional Model Quantum Cosmology 
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© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Center for Gravitation and Fundamental MetrologyVNIIMSMoscowRussia
  2. 2.Institute of Gravitation and Cosmology of Peoples’ Friendship University of RussiaMoscowRussia

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