Vacuum fluctuations of energy density can lead to the observed cosmological constant

Abstract

The energy density associated with the Planck length is ρ_UVα L^-4_P while the energy density associated with the Hubble length is ρ_IR αL^-4_H, where L_H = 1/H. The observed value of the dark energy density is quite different from either of these and is close to the geometric mean of the two: ρ_vac⋍√ρ_UVρ_IR. It is argued that classical gravity is actually a probe of the vacuum fluctuations of energy density rather than the energy density itself. While the globally defined ground state, being an eigenstate of the Hamiltonian, will not have any fluctuations, the ground-state energy in the finite region of space bounded by the cosmic horizon will exhibit fluctuations Δρ_vac(L_P, L_H). When used as a source of gravity, this Δρ should lead to a spacetime with a horizon size, L_H. This bootstrapping condition leads naturally to an effective dark energy density Δρ α (L_UVL_H)^-2 α H²/G, which is precisely the observed value. The model requires either (i) a stochastic fluctuation of vacuum energy which is correlated over about a Hubble time or (ii) a semi-anthropic interpretation. The implications are discussed.