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 previ...

in ordinary quantum mechanics for the position uncertainty since minimum value can be tend to zero. Different theories of gravity, such as string theory, loop and black hole physics, confirm a minimal observable length. Kempf et al have formulated The length is fundamental measurement, although there no lower bound generalized principle (GUP) by modifying Heisenberg include an appearance mechan...