Forgive me if I have this wrong. I have been reading about cosmology for 15 years and feel I still know precious little about it.

Anyway, if I am correct, equivalence tells us that gravity and acceleration are indistinguishable. As gravity is thought to be the consequence of the curvature of space-time, does that mean that accelerating objects cause space-time to curve? If so, is that what "frame dragging" is all about?