Accelerating Model of the Universe

I have questions about models of the universe that represent the growth
of the size of the universe with time. I know that the open model has
a hyperbolic shape and its density is between 0 and 1. The flat model
has no curvature and its density is equal to 1. The closed model has a
spherical shape and its density is greater than 1. What I can't find is
the accelerating model. My books have no information at all. My
questions are : 1. What is the shape of the accelerating model? What
is the density of the accelerating model? Which of the four models has
a universe full of dark energy causing the rate of expansion to increase
with time? My guess is the flat or open model.

Thanks to Odysseus for helping me last time. I got a perfect score on
the homework and a perfect score on the test.

Thanks in advance