  Some time ago we have suggested that positive vacuum energy exhibits a finite
quantum break time, which can be a signal that a positive cosmological constant
is inconsistent. From the requirement that Universe never undergoes through
quantum breaking, we have derived an absolute lower bound on the speed of
variation of positive vacuum energy. The same suggestion about exclusion of
positive cosmological constant was made recently. We show that the new bound
represents a particular string theoretic version of the old bound, which is
more general. In this light, we show that the existing window still provides a
large room for the inflationary and dark energy model building. In particular,
the inflationary models with gravitational strength interactions, are protected
against fast quantum breaking.

High Energy Physics - Theory;Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology