In article , Oh No
writes:

The cosmological parameters are pretty well tied down by supernova
observations, and that should tie q=q(t) down too.

Within the context of GR cosmology, knowing q_0 and Omega_0 (or
lambda_0, or any two independent cosmological parameters except H_0)
completely determines q(t).

The only thing is, q
is used in a series expansion, which we don't much use any more, and it

True. At small redshifts, q is the most important term, so historically
this was important. However, it is just Omega/2 - lambda, so is well
defined in a much larger context. Practically no modern cosmological
test "measures" q in the sense that the gradient of probability in
cosmological parameter space is shallowest along lines of constant q, so
this is another reason it is not used as often as it once was. However,
it does tell one whether or not the universe is accelerating.

makes not a lot of sense to use q(t) for any purpose I can think of.
What is usually discussed is q0=q(t0), i.e. now.

Right, though one might say something like "at a redshift of x,
corresponding to a time y years ago, the universe was still
decelerating".