Quantum Cosmology with Dynamical Vacuum in a Minimal-Length Scenario

In this work, we consider effects of the dynamical vacuum in quantum cosmology in presence of a minimum length introduced by the GUP (generalized uncertainty principle) related to the modified commutation relation $[\widehat{X},\widehat{P}]:=\frac{i\mathrm{\hslash }}{1-\beta {\widehat{P}}^2}$ . We determine the wave function of the Universe ${\psi }_{qp}(\xi ,t)$, which is solution of the modified Wheeler-DeWitt equation in the representation of the quasi-position space, in the limit where the scale factor of the Universe is small. Although ${\psi }_{qp}(\xi ,t)$ is a physically acceptable state it is not a realizable state of the Universe because ${\psi }_{qp}(\xi ,t)$ has infinite norm, as in the ordinary case with no minimal length.