  Based on quantum mechanical framework for the minimal length uncertainty, we
demonstrate that the generalized uncertainty principle (GUP) parameter could be
best constrained by recent gravitational waves observations on one hand. On
other hand this suggests modified dispersion relations (MDRs) enabling an
estimation for the difference between the group velocity of gravitons and that
of photons. Utilizing features of the UV/IR correspondence and the obvious
similarities between GUP (including non-gravitating and gravitating impacts on
Heisenberg uncertainty principle) and the discrepancy between the theoretical
and the observed cosmological constant (apparently manifesting gravitational
influences on the vacuum energy density), we suggest a possible solution for
the cosmological constant problem.
