  Very recently authors in [5] proposed a new Generalized Uncertainty Principle
(or GUP) with a linear term in Plank length. In this Letter the effect of this
GUP is studied in quantum cosmological models with dust and cosmic string as
the perfect fluid. For the quantum mechanical description it is possible to
find the wave packet which resulted from the superposition of the stationary
wave functions of the Wheeler-deWitt equation. However the norm of the wave
packets turned out to be time dependent and hence the model became non-unitary.
The loss of unitarity is due to the fact that the presence of the linear term
in Plank length in the Generalized Uncertainty Principle made the Hamiltonian
non-Hermitian.
