paper

Tunneling probability for the birth of an asymptotically DeSitter universe

arXiv:gr-qc/0612031 · doi:10.1103/PhysRevD.75.104004

Abstract

In the present work, we quantize a closed Friedmann-Robertson-Walker model in the presence of a positive cosmological constant and radiation. It gives rise to a Wheeler-DeWitt equation for the scale factor which has the form of a Schrödinger equation for a potential with a barrier. We solve it numerically and determine the tunneling probability for the birth of a asymptotically DeSitter, inflationary universe, initially, as a function of the mean energy of the initial wave-function. Then, we verify that the tunneling probability increases with the cosmological constant, for a fixed value of the mean energy of the initial wave-function. Our treatment of the problem is more general than previous ones, based on the WKB approximation. That is the case because we take into account the fact that the scale factor () cannot be smaller than zero. It means that, one has to introduce an infinity potential wall at , which forces any wave-packet to be zero there. That condition introduces new results, in comparison with previous works.

New version with a detailed comparison between our exact solution and previous WKB solutions. We show that they agree under certain conditions. Our treatment of the problem is more general than previous ones, based on the WKB approximation. That is the case because we take into account the fact that the scale factor () cannot be smaller than zero. It means that, one has to introduce an infinity potential wall at , which forces any wave-packet to be zero there. That condition introduces new results, in comparison with previous works. 17 pages (in revtex) and the previous 4 figures (in eps and ps)

References in corpus (1)

Cited by in corpus (10)