Quantum cosmology with dynamical vacuum in a minimal-length scenario

Abstract

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 $$[{\hat{X}},{\hat{P}}] := \frac{i\hbar }{ 1 - \beta {\hat{P}}^2 }$$ [ X ^ , P ^ ] : = i ħ 1 - β P ^ 2 . We determine the wave function of the Universe $$ \psi _{qp}(\xi ,t)$$ ψ qp ( ξ , 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 $$\psi _{qp}(\xi ,t)$$ ψ qp ( ξ , t ) is a physically acceptable state it is not a realizable state of the Universe because $$ \psi _{qp}(\xi ,t)$$ ψ qp ( ξ , t ) has infinite norm, as in the ordinary case with no minimal length.

Lorentzian vacuum transitions with a generalized uncertainty principle

“…Since this is an expected quantum feature it is natural to consider a GUP in superspace and look for solutions to the WDW equation. This has been studied in different scenarios before [37][38][39][40][41][42][43][44][45][46]. In particular in [45,46] it was studied the effects on GR as well as the Hořava-Lifshitz theory for a Kantowski-Sachs metric.…”