Recent astronomical observations of high redshift type Ia supernovae performed by two groups [1–3] as well as the power spectrum of the cosmic microwave background radiation obtained by the BOOMERANG [4] and MAXIMA-1 [5] experiments seem to indicate that at present the Universe is in a state of accelerated expansion. If one analyzes these data within the Friedmann–Robertson–Walker (FRW) standard model of cosmology their most natural interpretation is that the Universe is spatially flat and that the (baryonic plus dark) matter density ρ is about one third of the critical density ρcrit. Most interestingly, the dominant contribution to the energy density is provided by the cosmological constant Λ. The vacuum energy density (1.1)ρΛ≡Λ/(8πG) is about twice as large as ρ, i.e., about two thirds of the critical density. With ΩM≡ρ/ρcrit, ΩΛ≡ρΛ/ρcrit and Ωtot≡ΩM+ΩΛ: (1.2)ΩM≈1/3,ΩΛ≈2/3,Ωtot≈1. This implies that the deceleration parameter q is approximately −1/2. While originally the cosmological constant problem [6] was related to the question why Λ is so unnaturally small, the discovery of the important role played by ρΛ has shifted the emphasis toward the “coincidence problem”, the question why ρ and ρΛ happen to be of the same order of magnitude precisely at this very moment [7].
