“It’s not an “accelerating inflation””
Well, accelerating expansion, call it what you will. It’s happening and that means the problem remains. You can’t have an acceleration without an associated force, even though scientists don’t seem in any hurry to address that issue.
If the expansion is accelerating, it simply cannot be dismissed as an after-effect of the big bang, or the expansion would be either stable or decelerating. Acceleration means some undescribed force is currently driving it.
The nature of space-time is apparently such that it need not necessarily follow the ordinary laws of physics. ie, galaxies can and do expand away from each other faster than light speed. This is so because the galaxies are not actually moving through space but rather that the space between them is growing larger. The 'dimensionality', or 'measuring stick', is increasing in magnitude.