X iv : a st ro - p h / 99 04 22 1 v 1 1 6 A pr 1 99 9 Constraints on the cosmological constant from flows and supernovae

Recent measurements of the global curvature of space-time, using distant supernovae as distance indicators, favor a positive cosmological constant, associated with an accelerating universal expansion . However, these results by themselves still allow an open universe with low mass density and zero cosmological constant. We show here that this degeneracy is removed by independent constraints from galaxy peculiar velocities in our cosmological neighborhood, which provide a lower bound on the permissible mean mass density. The joint constraints from the two independent sources thus favor an unbound and nearly flat universe with comparable contributions from cosmological constant and mass density, and they rule out a low-density open universe of vanishing cosmological constant. The indicated conspiracy between the values of the cosmological constant and the mass density seems to require fine tuning that is in conflict with our common wisdom concerning the early universe. The standard cosmological model based on Einstein’s gravity and the anzats of global homogeneity is characterized by two fundamental dimensionless parameters that measure the main contributions to the total energy density (relative to a “critical” density): the mean mass density Ωm and the cosmological constant ΩΛ. The latter, an intrinsic part of the theory of General Relativity, represents a uniform energy density that is associated with the vacuum (as opposed to the mass), and, if positive, acts like a repulsive component of the global gravitational force. The values of these parameters determine the type of the universe we live in as follows. The Ωm-ΩΛ parameter plane shown in Figure 1 is divided by three dotted lines into six permissible regions. The line Ωm + ΩΛ = 1 defines a “flat”, Euclidean geometry, favored by theories of Inflation in the early universe. It separates curved models of “closed”, finite space (above) and “open”, infinite space (below). The horizontal line ΩΛ = 0 roughly distinguishes between an “unbound” universe that will expand forever (above) and a “bound” universe that will eventually re-collapse (below). Along the line ΩΛ = 0 itself, the