In article ,
(Gordon D. Pusch) writes:

Sadly, as others have already observed, a "cosmological constant" does
=NOT= lead to a "stable" universe, convecting or otherwise; it leads to
an UNSTABLE universe that undergoes either runaway expansion or collapse.
It is analogous to trying to balance a pencil on its point: The Universe
"wants" to fall over into either an implosion or explosion.

That's true. The same argument can be used against the Einstein-de
Sitter universe. Why it wasn't (until the discussion of the "flatness
problem" turned up a couple of decades ago) is an interesting historical
question. Of course, there are other arguments against the static
universe (such as the fact that the universe is expanding), but that
only strengthens the disbelief in this model, not the credibility of
other arguments against it.