Would it be workable if I update the steps in my post 234 like this, based on your comments? I followed your method of bolding the parameters, because it is clearer that way.

0. Set gas flow direction valve for inflating the balloon.

1. Continuously measure the radius R of the balloon and calculate (ΔR/dt)² = R²H² = R²Ho² ((1-Ω)/a² + Ω_m/a³ +Ω_r/a⁴ + Ω_Λ), with all the constants given and a = R/Ro, where Ro is a value that corresponds to the R for which the parameters are given.

1b. Calculate switch = (1-Ω)/a² + Ω_m/a³ +Ω_r/a⁴ + Ω_Λ. If switch goes negative, even temporarily, change the gas flow direction direction valve for permanently deflating the balloon. (??)

2. Measure ΔR/dt, square the result and compare it with the calculation of ΔR/dt².

3. If squared result is smaller than the calculation, increase gas flow rate.

4. If squared result is larger than the calculation, decrease gas flow rate.

5. Repeat from 1 until timed out (or something like that?)

It is an interesting exercise, but I still cannot figure what you want to do with it. You said you want to show applications. (?)

Regards.