We consider the hypothesis that the transition to an accelerated period in the current universe involves a quantum mechanical process. We identify a minisuperspace configuration with two Lorentzian sectors, separated by a classically forbidden region. The Hartle‐Hawking and Vilenkin wave functions are computed, together with the transition amplitudes towards the accelerating epoch. Furthermore, it is found that for specific initial conditions, the parameters characterizing the generalized Chaplygin gas become related through an expression involving an integern. We also introduce a phenomenological association between some brane world scenarios and a FRW minisuperspace cosmology with a generalized Chaplygin gas. Results suggest that the brane tension would become related to generalized Chaplygin gas parameters through another expression involving an integer. © 2004 American Institute of Physics