A Possible Solution of the Cosmological Constant Problem based on Minimal Length Uncertainty and GW170817 and PLANCK Observations

Abstract

We propose the generalized uncertainty principle (GUP) with an additional term of quadratic momentum motivated by string theory and black hole physics as 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 the gravitational waves observations; GW170817 event. Also, we suggest another proposal based on the modified dispersion relations (MDRs) in order to calculate the difference between the group velocity of gravitons and that of photons. We conclude that the upper bound reads $\beta_0 \simeq 10^{60}$. 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 $\Lambda$ (apparently manifesting gravitational influences on the vacuum energy density), known as {\it catastrophe of non-gravitating vacuum}, we suggest a possible solution for this long-standing physical problem, $\Lambda \simeq 10^{-47}~$GeV$^4/\hbar^3 c^3$.