Lorentzian vacuum transitions with a generalized uncertainty principle

Abstract The vacuum transition probabilities between to minima of a scalar field potential in the presence gravity are studied using Wentzel–Kramers–Brillouin approximation. First we propose method compute these by solving Wheeler–DeWitt equation semi-classical approach for any model superspace that contains terms squared as well linear momenta Hamiltonian constraint generalizing this way previous results. Then apply Friedmann–Lemaitre–Robertson–Walker (FLRW) metric with positive and null curvature Bianchi III when coordinates minisuperspace obey Standard Uncertainty Principle Generalized (GUP) is taken into account. In all cases compare results found effect considering GUP probability enhanced at first but it decays faster so corresponding scale factor big enough reduced. We also consider anisotropy result flat FLRW which corresponds its isotropy limit comment differences works.