Bounds on vacuum energy density in a general cosmological scenario

Abstract

General limits on the cosmological constant (or equivalently the vacuum energy density) are derived for an inflationary universe. This is accomplished under the general assumption of global hyperbolicity and without the use of any special properties like spherical symmetry or homogeneity ofthe underlying spacetime. Aclear upper limit of 1/3 is obtained for the vacuum energy density parameterQ~,while the lower limit is found to depend on the age of the oldest object in the universe.