A Possible Solution of the Cosmological Constant Problem Based on GW170817 and Planck Observations with Minimal Length Uncertainty

Abstract

We propose generalized uncertainty principle (GUP) with an additional term of quadratic momentum motivated by string theory and black hole physics and providing a quantum mechanical framework for the minimal length uncertainty, at the Planck scale. We demonstrate that the GUP parameter, ${\beta }_0$ , could be best constrained by the gravitational wave observations, GW170817 event. To determine the difference between the group velocity of graviton and that of the light, we suggest another proposal based on the modified dispersion relations (MDRs). We conclude that the upper bound of ${\beta }_0$ reads ≃1060. Utilizing features of the UV/IR correspondence and the apparent similarities between GUP (including nongravitating and gravitating impacts on Heisenberg uncertainty principle) and the discrepancy between the theoretical and the observed cosmological constant $\Lambda$ (obviously manifesting gravitational influences on the vacuum energy density), known as catastrophe of nongravitating vacuum, we suggest a possible solution for this long-standing physical problem, $\Lambda \simeq 10^{-47}$  GeV4/ℏ3c3.