  We propose two higher order generalized uncertainty principles(GUPs) which
predict a minimum uncertainty in momentum and apply the deformations that they
entail of the Heisenberg algebra to one half of the phase space of the LRS
Bianchi I models. After numerically solving the resultant Wheeler Dewitt
equations we analyze our solutions and provide evidence that potential IR
effects of quantum gravity could have played a role in selecting an
overwhelmingly likely geometrical configuration that a quantum universe can
possess. In addition we propose a GUP which predicts both a minimum uncertainty
in momentum and a maximal measurable length scale which can be interpreted as a
fixed maximum cosmological horizon. The results contained in this work provide
further incentives to study what effects higher order GUP(s) have on quantum
cosmology so we can obtain a better understanding of how quantum gravity could
have impacted cosmological evolution.
