Discussion of this over at PhysicsForums: Senovilla's Slowing Time Theory

What I understand is they're saying at the end of time, the universe will change from the appearance of a curved space (Lorentzian manifold) to a flat space (Euclidean manifold).

Interestingly I have read a book where the author derived the same notion via pure geometric intuition, the book is "Everything Forever: Learning to See Timelessness". Amazing read - you do not need to understand words like "AdS" or "brane-worlds" to read it, it's all geometry and plain intuition and analysis of simple observations.