Perhaps this is a naive question, but in my recent (admittedly limited) readings about AdS spaces, I keep wondering why they seem to be such a hotbed for theoretical research (AdS/CFT correspondence, etc.). To my understanding, an AdS space has constant negative curvature in a vacuum, which should yield an attractive universe, not one with accelerating expansion. An AdS space can be thought of as having a negative cosmological constant, while a universe with accelerating expansion would imply that such a constant be positive. Since we observe that our universe's expansion is accelerating, it seems that if anything, we should be seeking to model it as a de Sitter space.

Am I mistaken? What aspects of our universe do AdS spaces attempt to model?