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NONZERO Ω Λ AND A NEW TYPE OF THE DISSIPATIVE STRUCTURE ∗

We revisit the proposed theoretical model for a small but nonzero cosmological constant which seems supported increasingly better by recent observations. The model features two scalar fields which interact with each other through a specifically chosen nonlinear potential. We find a very sensitive dependence of the solutions of the scalar field equations on the initial values. We discuss how the behavior is similar to and different from those in well-known chaotic systems, coming to suggest an interesting new type of the dissipative structure. The cosmological constant problem has two faces; an upper bound and a lower bound. The former is given by the critical density ρcr, or ΩΛ ≡ Λ/ρcr < ∼1. In the Planckian unit system with 8πG = c = h̄ = 1, we know ρcr ≡ 3H 0 ∼ t 0 , and the present age of the universe t0 ∼ 10Gy is of the order of 10; hence the upper bound Λob < ∼10−120. On the other hand, almost any theoretical models of unification gives Λth ∼ 1. The discrepancy is the well-known disaster. Recent observations seem to indicate a lower bound as well; ΩΛ ∼ 0.7. Let us try to understand this “small but nonzero cosmological constant.” A solution for the upper bound may come from a scalar field φ of the Brans-Dicke type: L = √ −g ( 1 2 ξφR − 1 2 ǫg∂μφ∂νφ + Λ + Lmatter )