In article ,
writes:

But I used the modern co moving radii, then just multiplied by the ratio
of universe age, and am not sure the inversion is correct....ie, that
the expansion is (I think the term would be) reversible / self similar??

As I mentioned in another post, if you want what I think you want, just
forget the age and divide the current value by (1+z).

While what you mention above might hold in a special case, it is in
general certainly not true. Consider a universe which, at the
transition between the decelerating and accelerating phases, is almost
static. Yes, this requires fine-tuning of lambda and Omega, but is
possible and illustrates the point. The quasi-static phase can be
arbitrarily long, and the change in redshift (and hence scale factor)
arbitrarily small. So you could have a range in z between, say, 1.999
and 2.000 which corresponds to a trillion years.

Some things are hard, at least in the general case, such as calculating
distances from redshift or vice versa, calculating the scale factor as a
function of time, and so on. In general, these involve elliptic
integrals (or the inverse). On the other hand, some things can be done
with simple algebra. For example, given the current values of lambda
and Omega, it is simple (just based on their definitions) to calculate
the redshift at which they were equal.