Aspects of tunneling probability for the birth of an asymptotically DeSitter universe

Full text. 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 Schroedinger equation for a potential with a barrier. We solve it numerically using a finite difference procedure based on the Crank-Nicholson method, and implemented in the program GNU-OCTAVE. Our choice of the Crank-Nicholson method is based on its recognized stability. We introduce the computed wave-function in the general tunneling probability expression and evaluate it for the present model. It gives the probability for the birth of an 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. (author)