Isn't the apparent H-L change the reason that people think there was an acceleration in the rate of space expansion?
You're thinking logically.
But we have to go back to 1995 for this. There's a cool story behind all this.
The few articles addressing the tension, which is the small differences between the two expansion rates (today vs. 13.8 Gyrs ago via the CMBR) cause me to infer that the "surprise" is because they are not the same rate. Also of note, the differences are outside their respective margins of error. So it seems that the earlier rate (13.8 Gyrs ago) was actually a little less than today.
The original acceleration finding was big news in 1995. The two independent teams (Berkley & Harvard Obs.) studying Type 1a SN were conducted to improve the value of the expansion rate.
Berkly, comprised mainly of physicists, apparently had more clout and got the best telescopes and times to acquire a lot of SN data for distant galaxies. Harvard's team consisted mostly of astronomers. They wisely chose to use filtered imaging to improve their fit for their fewer data points. This gave them a more accurate result -- quality vs. quantity.
As a result, perhaps, Adam Reiss with the Harvard team broke the news that the universe is accelerating. Berkly announced it as well very shortly thereafter, perhaps the same or next day, IIRC.
This is when DE was born. Though no one then, nor today, knew the cause, it was easy to make the jump to an energy source since the cosmological constant -- a little DE from Einstein, if you will, to keep the cosmos from collapsing under its own "weight" -- never truly was discarded by all cosmologists. Recall that Edington, Lemaitre and, perhaps, de Sitter never tossed it, though Einstein felt it was too ad hoc and shown, in his view, to be superfluous once he recognized the elegance in Lemaitre's dynamic view of GR vs. his static model, which couldn't explain Slipher's redshifts. Also, Lemaitre's model actually included acceleration in his 1927 paper!
The recent studies, giving us "tension", of the acceleration rate at the time of the CMBR is slightly less. But no one I've seen so far has argued that a slower expansion rate should not have been predicted. I assume my lack of understanding is the reason, but how?
Space/time expansion and any acceleration is a theory based on observation, not a fact that has been proven by the observations.
Well, I like to reserve facts to represent objective evidence. Wishful thinking, suppositions, conjecture, hypotheses, theories come from these facts. The more facts, the stronger the theory, at least until the facts either force correction or destruction.
I'm guessing that a lot of people try to swallow too much when they first look at BBT. Thus, when I can present it, I prefer to simplify it and start with how it was found and work back from there.
Recall that Lemaitre had only two "facts": GR and galactic velocities/distance. [Three if we separate velocities and distances.]
In 1925, he started seeing error in deSitter's GR model, and began realizing that a dynamic model made more sense. [Weyl and Robertson also had dynamic models, but they didn't see the expansion, reportedly.] Lemaitre simply matched the galaxies having both Slipher's redshift velocities and Hubble's distance measurements, thus deriving the first linear relationship for galactic distance and recessional velocities. He labeled this expansion rate, ironically, H.
[When he translated the paper two years later into English, he left his expansion rate calculations out since, per his comments, Hubble had already improved the science on this. This likely is why Hubble has received so much of the credit, but a little too much, IMO.]
[Hubble took credit for this relationship, and he even blasted (Aug, 1930) de Sitter when he published his own, more advanced, linear relationship without giving enough credit, in Hubble's view, to Mt. Wilson (ie Hubble).]
And, its relationship to the gravitational constant "G" possibly also changing with time is even more hypothetical.
Might be true, but not a proven fact at this point in our development of understanding.
Perhaps, but if G is altered even a tiny, tiny, tiny bit in the earliest times, then either stars won't form (sllightly less G) or the Universe collapses.