Question re inflation and dark energy: current claims are that big-bang started with a very short period of inflation. Haven't heard/understood much on why infl

Question re inflation and dark energy: current claims are that big-bang started with a very short period of inflation. Haven't heard/understood much on why inflations started or stopped. Now we posit dark energy, that causes accelerated expansion of the universe, with acceleration greater at greater distances and therefore earlier historical times. So... is it possible that inflation and dark energy are related? When we see distant/ancient galaxies accelerating away from us, is there any chance we're looking at the ramping down of the original inflation of the big bang?