In article , Steve Willner
writes:

It would also lead to a
time dependence of the expansion contrary to observations,

In article ,
David Staup writes:
I thought we have seen a rate of expansion that is increasing over
time...no?

The observed change in expansion rate with time is consistent with a
cosmological constant, which I believe means that acceleration is
constant with time.

It's more complicated. At first, there is deceleration, then there is
acceleration, so neither is the rate of expansion constant with time,
but neither is the acceleration. However, the universe (and all
universes with a positive cosmological constant which don't collapse in
the future) will asymptotically approach the de Sitter universe, in
which the Hubble constant is constant in time (it is called the Hubble
constant not because it is generally constant in time, but because it is
a constant when fitting data points; the cosmological constant, however,
IS constant in time). However, the Hubble constant is the rate of
increase of the scale factor divided by the scale factor, so a constant
Hubble constant means an increasing acceleration in absolute terms
(exponential, in fact).

The technical description is that parameter w
has a value very close to -1.

Right. A pure cosmological constant has w=-1 exactly and there is no
observational evidence that this is not the case, and there is
observational evidence that it is quite close to -1.