Why do we observe a small but non zero cosmological constant?

Abstract

The current observations seem to suggest that the universe has a positive cosmological constant of the order of H²₀ while the most natural value for the cosmological constant will be L^-2_P, where L_P = (Għ/c³)^½ is the Planck length. This reduction of the cosmological constant from L^-2_P to L^-2_P(L_PH₀)² may be interpreted as due to the ability of quantum microstructure of spacetime to readjust itself and absorb bulk vacuum energy densities. Being a quantum-mechanical process, such a cancellation cannot be exact and the residual quantum fluctuations appear as the 'small' cosmological constant. I describe the features of a toy model for the spacetime microstructure which could allow for the bulk vacuum energy densities to be cancelled leaving behind a small residual value of the correct magnitude. Some other models (such as those based on the canonical ensemble for the 4-volume or quantum fluctuations of the horizon size) lead to an insignificantly small value of H²₀(L_PH₀)ⁿ with n = 0.5-1 showing that obtaining the correct order of magnitude for the residual fluctuations in the cosmological constant is a nontrivial task, because of the existence of the small dimensionless number H₀L_P.