Klein-Gordon Thermal Equation for a Preplanckian Universe
Abstract
In the paper the quantum hyperbolic equation formulated in [M. Kozlowski, J. Marciak-Kozlowska, From Quarks to Bulk Matter, Hadronic Press, 2001], is appled to the study of the propagation of the initial thermal state of the Universe. It is shown that the propagation depends on the barrier height. The Planck wall potential is introduced, VP=hbar/8tP=1.25 1018 GeV where tP is a Planck time. For the barrier height V<VP the master thermal equation is the modified Klein-Gordon equation and for barrier height V>VP the master equation is the Klein-Gordon equation. The solutions of both type equations for Cauchy boundary conditions are discussed.
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