  In this work we study the birth of Friedmann-Lema\^{\i}tre-Robertson-Walker
(FLRW) models with zero ($k=0$) and negative ($k=-1$) curvatures of the spatial
sections. The material content of the models is composed of a radiation perfect
fluid and a positive cosmological constant. The models also have the presence
of an ad hoc potential which origin is believed to be of geometrical nature. In
order to describe the birth of these universes, we quantize them using quantum
cosmology. Initially, we obtain the Wheeler-DeWitt equations and solve them
using the WKB approximation. We notice that the presence of the ad hoc
potential produces a barrier for any value of $k$. It means that we may
describe the birth of the universe through a tunneling mechanism, for any
curvature of the spatial sections, not only for the usual case $k=1$. We,
explicitly, compute the tunneling probabilities for the birth of the different
models of the universe and compare these tunneling probabilities.
