The possible effects of trans-Planckian physics on the scalar field in conformal inflation are investigated in the lattice Schrodinger picture. For the massless conformally coupled scalar field during the slow-roll inflation, we consider the Corley-Jacobson type dispersion relations with quartic or sextic correction to obtain the time evolution of the vacuum state wave functional. We then calculate explicitly the finite vacuum energy density due to fluctuations of the inflaton field, and evaluate the corresponding cosmological constant through the backreaction constraint on the magnitude of dispersion parameters. We also show how the cosmological constant reduces significantly during the slow-roll inflation at the grand unification phase transition. Finally, using the current astronomical observations which indicate that radiation and matter dominated epoch is sandwiched between two asymptotic de Sitter epochs, and knowing the fact that de Sitter geometry is invariant under time translation, we propose the possibility that similar reduction mechanism may reappear during the late time acceleration era, and thus yield a tiny current value of the cosmological constant.