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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 spatialsections. The material content of the models is composed of a radiation perfectfluid and a positive cosmological constant. The models also have the presenceof an ad hoc potential which origin is believed to be of geometrical nature. Inorder to describe the birth of these universes, we quantize them using quantumcosmology. Initially, we obtain the Wheeler-DeWitt equations and solve themusing the WKB approximation. We notice that the presence of the ad hocpotential produces a barrier for any value of $k$. It means that we maydescribe the birth of the universe through a tunneling mechanism, for anycurvature of the spatial sections, not only for the usual case $k=1$. We,explicitly, compute the tunneling probabilities for the birth of the differentmodels of the universe and compare these tunneling probabilities.

Tunneling probability for the birth of universes with radiation, cosmological constant and an ad hoc potential