2006/12/31 by J. Acácio de Barros, J. Acacio de Barros, E. V. Corrêa Silva +5 · 26 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Constant (computer programming) #Cosmological constant #Cosmology #Cosmology and Gravitation Theories #Dark energy #De Sitter universe #Mathematical physics #Metric expansion of space #Physics #Quantum Mechanics and Applications #Quantum mechanics #Quantum tunnelling #Scale factor (cosmology) #Universe #WKB approximation #Wave packet #gr-qc
paper · pdf · doi:10.1103/physrevd.75.104004
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 75(10) (American Physical Society) · 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 ($a$) cannot be smaller than zero. It means that, one has to introduce an infinity potential wall at $a = 0$, 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)
arxiv created 2007/03/28 · openalex publication_date 2007/05/07 · arxiv updated 2016/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 Schr"odinger 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 (a) cannot be smaller than zero. It means that, one has to introduce an infinity potential wall at a=0, which forces any wave packet to be zero there. That condition introduces new results, in comparison with previous works.