Vacuum Fluctuations of Energy Density can lead to the observed Cosmological Constant

The energy density associated with Planck length is $\rho_{uv}\propto L_P^{-4}$whiletheenergydensityassociatedwiththeHubblelengthis$\rho_{ir}\propto L_H^{-4}$where$L_H=1/H$. The observed value of the dark energy density is quite different from {\it either} of these and is close to the geometric mean of the two: ${\rho }_{vac}\simeq \sqrt{{\rho }_{uv}{\rho }_{ir}}$. It is argued that classical gravity is actually a probe of the vacuum {\it fluctuations} of energy density, rather than the energy density itself. While the globally defined ground state, being an eigenstate of Hamiltonian, will not have any fluctuations, the ground state energy in the finite region of space bounded by the cosmic horizon will exhibit fluctuations $\Delta\rho_{\rm vac}(L_P, L_H)$\mathrm{.}Whenusedasasourceofgravity,this$\Delta \rho$ should lead to a spacetime with a horizon size $L_H$. This bootstrapping condition leads naturally to an effective dark energy density $\Delta\rho\propto (L_{uv}L_H)^{-2}\propto H^2/G$ which is precisely the observed value. The model requires, either (i) a stochastic fluctuations of vacuum energy which is correlated over about a Hubble time or (ii) a semi- anthropic interpretation. The implications are discussed.