Explaining accelerating spacetime expansion?

I should begin by noting that I am NOT a physicist, I study differential geometry and so my physics background is extremely limited. That being said I was reading a textbook on general relativity and found the idea of the expansion of the universe and the cosmological constant rather interesting. I study a lot of hyperbolic manifolds, and although it is generally not considered that the universe has negative curvature, is it possible that constant expansion could appear as though it is accelerating in a hyperbolic universe? In other words, could the universe be expanding at a constant rate, but negative curvature induces a psuedo-acceleration that is caused by contraction of lengths and negative curvature?