In article , Steve Willner
writes:

In article ,
Phillip Helbig---undress to reply writes:
At first, there is deceleration, then there is
acceleration,

What I meant was that acceleration _owing to a cosmological constant_
is constant in time.

OK, there is an overlap between deceleration due to matter and
acceleration due to the cosmological constant. Matter thins out with
time so acceleration takes over.

At least I believe that's the case,

It's not. Consider the de Sitter universe, which has a cosmological
constant and no matter. The expansion law is exponential, i.e. the
acceleration increases with time. Since the Hubble constant is
dr/dt*1/R, it is constant in time. The parameter q is constant at -1.
It is defined as \frac{-\ddot R R}{\dot R^{2}} or
\frac{-\ddot R}{RH^{2}}. Since H is constant in time, \ddot R must
increase with time in proportion to R. So, of course, as with any
exponential, all derivatives are exponential.

but I've
never had a proper course in modern cosmology.

I still recommend three books: Edward Harrison's COSMOLOGY: THE SCIENCE
OF THE UNIVERSE, Bondi's COSMOLOGY and Berry's COSMOLOGY AND
GRAVITATION. Of course, these won't contain details of the CMB etc, but
partially for that reason they are good on the foundations. A good
historical overview, starting in the mists of time but with an emphasis
on the twentieth century, is Barrow's THE BOOK OF UNIVERSES.

If the dark energy is
something other than (or in addition to) a cosmological constant, the
time dependence of its acceleration is likely to be different.

Right. That's pretty much the definition of "dark energy".