The term the synthesis of glycogen isn't common enough to draw meaningful conclusions by searching NGrams (chart-based interface into the vast Google Books corpus), but here's what I found using protein synthesis...
Maybe it's just that to accelerate sounds more "professional, academic" than to speed up (there's certainly no semantic difference). But the preference is obviously quite strong, given the latter doesn't even occur often enough to show on the chart.
I didn't bother including quicken or hasten as per the other answer here, because they're so unlikely. (Not least because nobody talked about "protein synthesis" back in Victorian times when those verbs might have been used in similar contexts! :)
But note that in more colloquial / conversational contexts, speed up is a vastly more common "opposite" to slow down (which in academia might more often be expressed as retard, inhibit).
TLDR: The standard term is "accelerate". Forget about looking for an alternative.