In a quantitative science verbal phrases like "rate of expansion" have to correspond to mathematically well-defined quantities. As far as I know, in Cosmology the only quantitative handle in common use that corresponds to "rate of cosmic expansion" is the Hubble constant, and as best we can tell it has been declining over time since around the start of expansion. According to the standard cosmic model it is expected to continue declining but not to zero. The declining rate of expansion H(t) is expected to level out at a positive value H∞. That is the effect of the cosmological constant, in fact H∞2 = Λc2/3. You could say that the cosmo constant Λ is just an alternative form of the longterm expansion rate H∞---or vice versa the longterm expansion rate is a concrete practical expression for "dark energy" alias the cosmo constant. I was struck by the seeming confusion that arose in another thread, that began with this clear straightforward question by one of our members. The discussion seemed to get lost amid ill-defined or purely verbal expressions. I'd like to make a fresh start on that and deal with it in well-defined definite quantitative terms from the very start. Maybe others would like to help, or take over at this point, for that matter.